|
Iteration of meromorphic functions
Author(s):
Walter
Bergweiler
Journal:
Bull. Amer. Math. Soc.
29
(1993),
151-188.
MSC (2000):
Primary 30D05, 58F08;
Secondary 30D30, 65H05
MathSciNet review:
1216719
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- *
- {Aar91} J. M. Aarts and L. Oversteegen,{\em The geometry of Julia sets\/},Trans. Amer. Math. Soc. {\bf338} (August 1993). MR 1182980
- *
- {Ahl35} L. V. Ahlfors, {\em Zur Theorie der \"Uberlagerungsfl\"achen\/},Acta Math. {\bf65} (1935), 157--194. MR 1555403
- *
- {Ahl73} \bysame, {\em Conformal invariants},McGraw-Hill, New York, 1973. MR
- *
- {Bak59} I. N. Baker, {\em Fixpoints and iterates of entirefunctions\/}, Math. Z. {\bf71} (1959), 146--153. MR 107015
- *
- {Bak59-60} \bysame, {\em Some entire functionswith fixpoints of every order\/},J. Australian Math. Soc. {\bf1} (1959/60), 203--209. MR 114007
- *
- {Bak60} \bysame, {\em The existence of fixpointsof entire functions\/}, Math. Z. {\bf73} (1960), 280--284. MR 114008
- *
- {Bak63} \bysame, {\em Multiply connected domains of normality in iteration theory\/},Math. Z. {\bf81} (1963), 206--214. MR 153842
- *
- {Bak64} \bysame, {\em Fixpoints of polynomials and rational functions\/},J. London Math. Soc. (2) {\bf39} (1964), 615--622. MR 169989
- *
- {Bak65} \bysame, {\em Sets of non-normality in iteration theory\/},J. London Math. Soc. (2) {\bf40} (1965), 499--502. MR 180668
- *
- {Bak68} \bysame, {\em Repulsive fixpointsof entire functions\/}, Math. Z. {\bf104} (1968), 252--256. MR 226009
- *
- {Bak70}\bysame, {\em Limit functions and sets of non-normality in iteration theory\/},Ann. Acad. Sci. Fenn. Ser. A I Math.{\bf467} (1970). MR 264071
- *
- {Bak70a}\bysame, {\em Completely invariant domains of entirefunctions\/},Mathematical Essays Dedicated to A. J. Macintyre,(H. Shankar, ed.),Ohio Univ. Press, Athens, Ohio, 1970, pp. 33--35. MR
- *
- {Bak75}\bysame, {\em The domains of normality of an entire function\/},Ann. Acad. Sci. Fenn. Ser. A I Math.{\bf1} (1975), 277--283. MR 402044
- *
- {Bak76}\bysame, {\em An entire function which has wandering domains\/},J. Austral. Math. Soc. Ser. A {\bf22} (1976), 173--176. MR 419759
- *
- {Bak81}\bysame, {\em The iteration of polynomials and transcendental entire functions\/},J. Austral. Math. Soc. Ser. A {\bf30} (1981), 483--495. MR 621564
- *
- {Bak84}\bysame, {\em Wandering domains in the iteration of entire functions\/},Proc. London Math. Soc. (3) {\bf49} (1984), 563--576. MR 759304
- *
- {Bak85}\bysame, {\em Some entire functions withmultiply-connected wandering domains\/},Ergodic Theory Dynamical Systems {\bf5} (1985), 163--169. MR 796748
- *
- {Bak87} \bysame, {\em Iteration of entire functions\/}\,:{\em an introductory survey\/}, Lectures on Complex Analysis,World Scientific,Singapore, New Jersey, London, and Hong Kong, 1987, pp. 1--17. MR 996465
- *
- {Bak87a}\bysame, {\em Wandering domains for maps of the punctured plane\/},Ann. Acad. Sci. Fenn. Ser. A I Math.{\bf12} (1987), 191--198. MR 951969
- *
- {Bak88}\bysame, {\em Infinite limits in the iteration of entire functions\/},Ergodic Theory Dynamical Systems {\bf8} (1988), 503--507. MR 980793
- *
- {Bak91}I. N. Baker, J. Kotus, and Y. L\"u,{\em Iterates of meromorphic functions.} I,Ergodic Theory Dynamical Systems {\bf11} (1991), 241--248. MR 1116639
- *
- {Bak90b} \bysame, {\em Iterates of meromorphic functions\/} II: {\em Examples of wandering domains\/},J. London Math. Soc. (2) {\bf42} (1990), 267--278. MR 1083445
- *
- {Bak91a}\bysame, {\em Iterates of meromorphic functions\/} III: {\em Preperiodic domains\/},Ergodic Theory Dynamical Systems {\bf11} (1991), 603--618. MR 1145612
- *
- {Bak92}\bysame, {\em Iterates of meromorphic functions\/} IV: {\em Critically finite functions\/},Results Math. {\bf22} (1992), 651--656. MR 1189754
- *
- {Bak84a}\bysame, {\em Iteration of exponential functions\/},Ann. Acad. Sci. Fenn. Ser. A I Math.{\bf9} (1984), 49--77. MR 752391
- *
- {Bar55} B. Barna,{\em \"Uber die Divergenzpunkte des Newtonschen Verfahrens zurBestimmung von Wurzeln von algebraischen Gleichungen\/} II,Publ. Math. Debrecen {\bf4} (1955/56), 384--397. MR 78956
- *
- {Bea91} A. F. Beardon,{\em Iteration of rational functions},Springer, New York, Berlin, and Heidelberg, 1991. MR 1128089
- *
- {Ber90} W. Bergweiler, {\em On the number of fix-points ofiterated entire functions\/}, Arch. Math. {\bf55} (1990), 558--563. MR 1078277
- *
- {Ber91}\bysame, {\em Periodic points of entire functions\/}\,: {\em proof of a conjecture of Baker\/},Complex Variables Theory Appl. {\bf17} (1991), 57--72. MR 1123803
- *
- {Ber92}\bysame, {\em On the existence of fixpoints ofcomposite meromorphic functions\/},Proc. Amer. Math. Soc. {\bf114} (1992), 879--880. MR 1091176
- *
- {Ber92a}\bysame, {\em Newton\rom{'}s method and a class of meromorphic functions without wanderingdomains\/},Ergodic Theory Dynamical Systems (to appear). MR
- *
- {Ber91a} W. Bergweiler, F. von Haeseler, H. Kriete, H.-G. Meier,and N. Terglane,{\em Newton\rom{'}s method for meromorphic functions\/},Proceedings of the conference ``Complex analysis and itsapplications'', Hong Kong (to appear). MR 1278929
- *
- {Ber92b} W. Bergweiler, M. Haruta, H. Kriete, H.-G. Meier,and N. Terglane,{\em On the limit functions of iterates in wandering domains\/},Ann. Acad. Sci. Fenn. Ser. A I Math.(to appear). MR 1234740
- *
- {Ber93} W. Bergweiler and S. Rohde,{\em Omitted values in domains of normality\/}, preprint. MR 1249869
- *
- {Ber92c} W. Bergweiler and N. Terglane,{\em Weakly repelling fixpoints and the connectivity of wandering domains\/},preprint. MR 1327252
- *
- {Bha69} P. Bhattacharyya,{\em Iteration of analytic functions},Ph.D. thesis, Univ. of London, 1969. MR
- *
- {Bla84} P. Blanchard, {\em Complex analytic dynamicson the Riemann sphere\/}, Bull. Amer. Math. Soc.(N.S.) {\bf11} (1984), 85--141. MR 741725
- *
- {Boe98} L. E. B\"ottcher,{\em Beitr\"age zu der Theorie der Iterationsrechnung},Inaugural dissertation, Leipzig, 1898. MR
- *
- {Bra89} D. A. Brannan and W. K. Hayman,{\em Research problems in complex analysis\/},Bull. London Math. Soc. {\bf21} (1989), 1--35. MR 967787
- *
- {Bro67} H. Brolin, {\em Invariant sets under iteration ofrational functions\/}, Ark. Mat. {\bf6} (1967), 103--141. MR 194595
- *
- {Bul90} W. D. Bula and L. Oversteegen,{\em A characterization of smooth Cantor bouquets\/},Proc. Amer. Math. Soc. {\bf108} (1990), 529--534. MR 991691
- *
- {Car90} L. Carleson and T. W. Gamelin,{\em Complex dynamics},Springer, New York, Berlin, and Heidelberg, 1993. MR 1230383
- *
- {Ceb28} N. G. \v{C}ebotarev,{\em\"Uber die Realit\"at von Nullstellen ganzer transzendenter Funktionen\/},Math. Ann. {\bf99} (1928), 660--686. MR 1512472
- *
- {Chu85} C.-T. Chuang,{\em A simple proof of a theorem of Fatou on the iteration and fix-pointsof transcendental entire functions\/},Analytic Functions of One Complex Variable,(C.-C. Yang and C.-T. Chuang, eds.),Contemp. Math., vol. 48, Amer. Math. Soc.,Providence, RI, 1985, pp. 65--69. MR 838099
- *
- {Clu70} J. Clunie, {\em The composition of entire and meromorphicfunctions\/}, Mathematical Essays Dedicated to A. J. Macintyre(H. Shankar, ed.),Ohio Univ. Press, Athens, Ohio, 1970, pp. 75--92. MR 271352
- *
- {Cre25} H. Cremer,{\em \"Uber die Iteration rationaler Funktionen\/},Jahresber. Deutsche Math.-Ver. {\bf33} (1925), 185--210. MR
- *
- {Cre28}\bysame, {\em Zum Zentrumsproblem\/},Math. Ann. {\bf98} (1926), 151--163. MR
- *
- {Cre32}\bysame, {\em \"Uber die Schr\"odersche Funktionalgleichungund das Schwarzsche Eckenabbildungsproblem\/},Ber. Verh. S\"achs. Akad. Wiss. Leipzig, Math.-Phys. Kl.{\bf84} (1932), 291--324. MR
- *
- {Cre38}\bysame, {\em \"Uber die H\"aufigkeit der Nichtzentren\/},Math. Ann. {\bf115} (1938), 573--580. MR 1513203
- *
- {Dev84a} R. L. Devaney,{\em Julia sets and bifurcation diagrams for exponential maps\/},Bull. Amer. Math. Soc. (N.S.) {\bf11} (1984), 167--171. MR 741732
- *
- {Dev85}\bysame, {\em Structural instability of $\exp(z)$\/},Proc. Amer. Math. Soc. {\bf94} (1985), 545--548. MR 787910
- *
- {Dev86}\bysame, {\em Dynamics of entire maps\/},Dynamical Systems and Ergodic Theory, Banach Center Publ.,vol. 23, Polish Scientific Publishers, Warsaw, 1989,pp. 221--228. MR 1102716
- *
- {Dev89a}\bysame, {\em An introduction to chaotic dynamical systems},second ed.,Addison-Wesley, Redwood City, 1989. MR
- *
- {Dev89b}\bysame, {\em Film and video as a research tool\/},Math. Intelligencer {\bf11} (1989), 33--38. MR 994962
- *
- {Dev89c}\bysame, {\em Dynamics of simple maps\/}, Chaos and Fractals. The Mathematics Behind the Computer Graphics(R. L. Devaney and L. Keen, eds.),Amer. Math. Soc., Providence, RI, 1989, pp. 1--24. MR 1010233
- *
- {Dev91a}\bysame, $e^z$: {\em Dynamics and bifurcations\/},Internat. J. Bifurcation Chaos {\bf1} (1991), 287--308. MR 1120198
- *
- {Dev91} R. L. Devaney and M. B. Durkin,{\em The exploding exponential and other chaotic bursts in complex dynamics\/},Amer. Math. Monthly {\bf98} (1991), 217--232. MR 1093952
- *
- {Dev86b} R. L. Devaney, L. R. Goldberg, and J. Hubbard,{\em Dynamical approximation to the exponential map by polynomials\/},Preprint MSRI 10019-86,Mathematical Sciences Research Institute, Berkeley, CA, 1986. MR
- *
- {Dev89} R. L. Devaney and L. Keen,{\em Dynamics of meromorphicmaps with polynomial Schwarzian derivative\/},Ann. Sci. \'Ecole Norm. Sup. (4) {\bf22} (1989), 55--81. MR 985854
- *
- {Dev84} R. L. Devaney and M. Krych,{\em Dynamics of $\exp(z)$\/},Ergodic Theory Dynamical Systems {\bf4} (1984), 35--52. MR 758892
- *
- {Dev86a} R. L. Devaney and F. Tangermann,{\em Dynamics of entire functions near the essential singularity\/},Ergodic Theory Dynamical Systems {\bf6} (1986), 489--503. MR 873428
- *
- {Dou82} A. Douady and J. H. Hubbard,{\em It\'eration des polyn\^omes quadratiques complexes\/},C. R. Acad. Sci. Paris S\'er. I {\bf294} (1982), 123--126. MR 651802
- *
- {Dou84}\bysame, {\em \'Etude dynamique des polyn\^omes complexes. \rom{I \& II}},Publ. Math. Orsay 84-02 (1984) \& 85-04 (1985). MR
- *
- {Dou91} N. Doual, J. L. Howland, and R. Vaillancourt,{\em Selective solutions of transcendental equations\/},Computers Math. Appl. {\bf22} (1991), 61--76. MR 1136170
- *
- {Edr55} A. Edrei,{\em Meromorphic functions with three radially distributed values\/},Trans. Amer. Math. Soc. {\bf78} (1955), 276--293. MR 67982
- *
- {Ere89} A. E. Eremenko, {\em On the iteration of entire functions\/},Dynamical Systems and Ergodic Theory, Banach Center Publ.,vol. 23, Polish Scientific Publishers, Warsaw, 1989, pp. 339--345. MR 1102727
- *
- {Ere84} A. E. Eremenko and M. Yu. Lyubich,{\em Iterates of entire functions\/},Soviet Math. Dokl. {\bf30} (1984), 592--594; translation fromDokl. Akad. Nauk. SSSR {\bf279} (1984). MR 769199
- *
- {Ere87}\bysame, {\em Examples of entire functions with pathological dynamics\/},J. London Math. Soc. (2) {\bf36} (1987), 458--468. MR 918638
- *
- {Ere90}\bysame, {\em The dynamics of analytic transforms\/},Leningrad Math. J. {\bf1} (1990), 563--634. MR 1015124
- *
- {Ere90a}\bysame, {\em Dynamical properties of some classes of entire functions\/},Ann. Inst. Fourier (Grenoble) {\bf42} (1992), 989--1020. MR 1196102
- *
- {Fat19} P. Fatou, {\em Sur les \'equations fonctionelles\/},Bull. Soc. Math. France {\bf47} (1919), 161--271;{\bf48} (1920), 33--94, 208--314. MR
- *
- {Fat26}\bysame, {\em Sur l\rom{'}it\'eration des fonctions transcendantesenti\`eres\/}, Acta Math. {\bf47} (1926), 337--360. MR
- *
- {Fle89} M. Flexor and P. Sentenac,{\em Algorithmes de Newton g\'en\'eralis\'es\/},C. R. Acad. Sci. Paris S\'er. I Math. {\bf308} (1989), 445--448. MR 991879
- *
- {Ghy85} E. Ghys, L. R. Goldberg, and D. P. Sullivan,{\em On the measurable dynamics of $z\to e^z$\/},Ergodic Theory Dynamical Systems {\bf5} (1985), 329--335. MR 805833
- *
- {Gol86} L. R. Goldberg and L. Keen,{\em A finiteness theorem for a dynamical class of entire functions\/},Ergodic Theory Dynamical Systems {\bf6} (1986), 183--192. MR 857196
- *
- {Hae91} F. von Haeseler and H. Kriete,{\em The relaxed Newton\RM's method for polynomials\/},preprint. MR
- *
- {Hae88} F. von Haeseler and H.-O. Peitgen,{\em Newton\rom{'}s method and complex dynamical systems\/},Acta Appl. Math. {\bf13} (1988), 3--58;{\em Newton\rom{'}s method and dynamical systems\/}(H.-O. Peitgen, ed.), Kluwer Academic Publishers, Dordrecht, 1989, pp. 3--58. MR 979816
- *
- {Har92} M. Haruta,{\em The dynamics of Newton\rom{'}s method on the exponential functionin the complex domain}, Ph.D. thesis, Boston Univ., 1992. MR
- *
- {Hay64} W. K. Hayman,{\em Meromorphic functions},Clarendon Press, Oxford, 1964. MR 164038
- *
- {Hay74}\bysame, {\em The local growth of power series\/}\,:{\em a survey of the Wiman-Valiron method\/},Canad. Math. Bull. (3) {\bf17} (1974),317--358. MR 385095
- *
- {Her84} M. Herman, {\em Exemples de fractions rationelles ayantune orbite dense sur la sph\`ere de Riemann\/},Bull. Soc. Math. France {\bf112} (1984), 93--142. MR 771920
- *
- {Her85}\bysame, {\em Are there critical points on the boundary of singular domains\/}\,?,Comm. Math. Phys. {\bf99} (1985), 593--612. MR 796014
- *
- {Hin92} A. Hinkkanen,{\em Iteration and the zeros of the second derivative of a meromorphicfunction\/},Proc. London Math. Soc.(3) {\bf65} (1992), 629--650. MR 1182104
- *
- {Hin92a}\bysame, {\em On the size of Julia sets\/}, preprint. MR
- *
- {How85} J. L. Howland and R. Vaillancourt,{\em Attractive cycles in the iteration of meromorphic functions\/},Numer. Math. {\bf46} (1985), 323--337. MR 791694
- *
- {How90} J. L. Howland, A. Thompson,and R. Vaillancourt,{\em On the dynamics of a meromorphic function\/},Appl. Math. Notes {\bf15} (1990), 7--37. MR 1102745
- *
- {Jan85} G. Jank and L. Volkmann,{\em Einf\"uhrung in die Theorie der ganzen und meromorphenFunktionen mit Anwendungen auf Differentialgleichungen}, Birkh\"auser,Basel, Boston, and Stuttgart, 1985. MR 820202
- *
- {Jon88} H. Th. Jongen, P. Jonker, and F. Twilt,{\em The continuous, desingularized Newton method for meromorphic functions\/},Acta Appl. Math. {\bf13} (1988), 82--121;{\em Newton\rom{'}s method and dynamical systems}(H.-O. Peitgen, ed.),Kluwer Academic Publishers, Dordrecht 1989,pp. 82--121. MR 979818
- *
- {Jul18} G. Julia, {\em Sur l\rom{'}it\'eration des fonctions rationelles\/},J. Math. Pures Appl. (7) {\bf4} (1918), 47--245. MR
- *
- {Jul18a}\bysame, {\em Sur des probl\`emes concernantl'it\'eration des fonctions rationelles\/},C. R. Acad. Sci. Paris S\'er. I. Math. {\bf166} (1918), 153--156. MR
- *
- {Kee88} L. Keen,{\em Dynamics of holomorphic self-maps of $\C^*$\/},Holomorphic Functions and Moduli. I(D. Drasin, C. J. Earle, F. W. Gehring,I. Kra, and A. Marden, eds.),Springer, New York, Berlin, and Heidelberg, 1988. MR 955806
- *
- {Kee89}\bysame, {\em Topology and growth of a special class of holomorphic self-mapsof $\C^*$\/},Ergodic Theory Dynamical Systems {\bf9} (1989), 321--328. MR 1007413
- *
- {Kee89a}\bysame, {\em Julia sets\/},Chaos and Fractals. The Mathematics Behind the ComputerGraphics(R. L. Devaney and L. Keen, eds.),Amer. Math. Soc., Providence, RI, 1989, pp. 57--74. MR 1010236
- *
- {Kot87} J. Kotus,{\em Iterated holomorphic maps of the punctured plane\/},Dynamical Systems,(A. B. Kurzhanski and K. Sigmund, eds.),Lecture Notes Econom. and Math. Systems, vol. 287,Springer, Berlin, Heidelberg, and New York, 1987, pp. 10--29. MR 1120038
- *
- {Kot90}\bysame, {\em The domains of normality of holomorphic self-maps of $\C^*$\/},Ann. Acad. Sci. Fenn. Ser. A I Math.{\bf15} (1990), 329--340. MR 1087340
- *
- {Kra93} B. Krauskopf,{\em Convergence of Julia sets in the approximation of $\lambda e^z$by $\lambda (1+\frac{z}{d})^d$\/},Internat. J. Bifurcation Chaos (to appear). MR 1232971
- *
- {Kri92} H. Kriete,{\em On the efficiency of relaxed Newton\rom{'}s method\/},Proceedings of the conference ``Complex analysis and itsapplications'', Hong Kong (to appear). MR 1278935
- *
- {Lat18} S. Latt\`es,{\em Sur l\rom{'}it\'eration des substitutions rationelles et les fonctionsde Poincar\'e\/},C. R. Acad. Sci. Paris Ser. I Math. {\bf166} (1918), 26--28 (Errata: p. 88). MR
- *
- {Leh65} O. Lehto and K. I. Virtanen,{\em Quasikonforme Abbildungen},Springer, Berlin, Heidelberg, and New York, 1965. MR 188434
- *
- {Lyu86} M. Yu. Lyubich, {\em The dynamics of rational transforms\/\,\RM:the topological picture\/}, Russian Math. Surveys {\bf41} (1986), 43--117;translation from Uspekhi Mat. Nauk. {\bf41}(1986), 35--95. MR 863874
- *
- {Lyu87}\bysame,{\em Measurable dynamics of the exponential\/},Soviet Math. Dokl. {\bf35} (1987), 223--226; translation fromDokl. Akad. Nauk. SSSR {\bf292} (1987). MR 880612
- *
- {Lyu88}\bysame, {\em Measurable dynamics of the exponential\/},Sib. Math. J. {\bf28} (1988), 780--793; translation fromSib. Mat. Zh. {\bf28} (1987), 111--127. MR 924986
- *
- {McM87} C. McMullen,{\em Area and Hausdorff dimension of Julia sets of entire functions\/},Trans. Amer. Math. Soc. {\bf300} (1987), 329--342. MR 871679
- *
- {Mak88} P. M. Makienko,{\em Iterates of analytic functions of $\C^*$\/},Soviet Math. Dokl. {\bf36} (1988), 418--420; translation fromDokl. Akad. Nauk. SSSR {\bf297} (1987). MR 916928
- *
- {May76} R. M. May,{\em Simple mathematical models with very complicated dynamics\/},Nature {\bf261} (1976), 459--467. MR
- *
- {May90} J. C. Mayer,{\em An explosion point for the set of endpoints of the Julia setof $\lambda\exp(z)$\/},Ergodic Theory Dynamical Systems {\bf10} (1990), 177--183. MR 1053806
- *
- {Mei91} H.-G. Meier,{\em The relaxed Newton-iteration for rational functions\/\,\RM: the limiting case\/},Complex Variables Theory Appl. {\bf16} (1991), 239--260. MR 1105199
- *
- {Mil90} J. Milnor,{\em Dynamics in one complex variable\/\,\RM: introductory lectures\/},Stony Brook Institute for Mathematical Sciences, preprint 1990/5. MR 1721240
- *
- {Mis81} M. Misiurewicz,{\em On iterates of $e^z$\/},Ergodic Theory and Dynamical Systems {\bf1} (1981), 103--106. MR 627790
- *
- {Mon27} P. Montel,{\em Le\c{c}ons sur les familles normales de fonctions analytiqueset leurs applications},Gauthiers-Villars,Paris, 1927. MR
- *
- {Nev70} R. Nevanlinna,{\em Analytic functions},Springer, Berlin, Heidelberg, and New York, 1970. MR 279280
- *
- {Pei86} H.-O. Peitgen and P. H. Richter,{\em The beauty of fractals}, Springer,Berlin, Heidelberg, New York, and Tokyo, 1986. MR 852695
- *
- {Per92} R. P\'erez-Marco,{\em Solution compl\`ete au probl\`eme de Siegel de lin\'earisationd\rom{'}une application holomorphe au voisinage d\rom{'}un point fixe\/}({\em d\rom{'}apr\`es J.-C. Yoccoz\/}),S\'em. Bourbaki {\bf753} (1992). MR
- *
- {Rad53}H. Radstr\"om,{\em On the iteration of analytic functions\/},Math. Scand. {\bf1} (1953), 85--92. MR 56702
- *
- {Ree86} M. Rees,{\em The exponential map is not recurrent\/},Math. Z. {\bf191} (1986), 593--598. MR 832817
- *
- {Rit20} J. F. Ritt,{\em On the iteration of rational functions\/},Trans. Amer. Math. Soc. {\bf21} (1920), 348--356. MR 1501149
- *
- {Ros48} P. C. Rosenbloom, {\em L\rom{'}it\'eration des fonctionsenti\`eres\/}, C. R. Acad. Sci. ParisS\'er. I Math. {\bf227} (1948), 382--383. MR 26691
- *
- {Rue89} D. Ruelle,{\em Elements of differentiable dynamics and bifurcation theory},Academic Press, Boston, 1989. MR 982930
- *
- {Sie42} C. L. Siegel,{\em Iteration of analytic functions\/},Ann. of Math. (2) {\bf43} (1942), 607--612. MR 7044
- *
- {Sil88} M. Viana da Silva,{\em The differentiability of the hairs of $\exp(z)$\/},Proc. Amer. Math. Soc. {\bf103} (1988), 1179--1184. MR 955004
- *
- {Shi87} M. Shishikura, {\em On the quasi-conformal surgeryof rational functions\/}, Ann. Sci. \'Ecole Norm. Sup. (4){\bf20} (1987), 1--29. MR
- *
- {Shi90}\bysame, {\em The connectivity of the Julia set and fixed point\/},preprint IHES/M/90/37, Institut des Hautes \'Etudes Scientifiques, 1990. MR
- *
- {Sma85} S. Smale,{\em On the efficiency of algorithms of analysis\/},Bull. Amer. Math. Soc. (N.S.) {\bf13} (1985), 87--121. MR 799791
- *
- {Sta90} G. M. Stallard,{\em Entire functions with Julia sets of zero measure\/},Math. Proc. Cambridge Philos. Soc. {\bf108} (1990), 551--557. MR 1068456
- *
- {Sta91}\bysame, {\em A class of meromorphic functions with no wandering domains\/},Ann. Acad. Sci. Fenn. Ser. A I Math.{\bf16} (1991), 211--226. MR 1139794
- *
- {Sta91a}\bysame, {\em The Hausdorff dimension of Julia sets of entire functions\/},Ergodic Theory Dynamical Systems {\bf11} (1991), 769--777. MR 1145621
- *
- {Ste90} N. Steinmetz,{\em On Sullivan\rom{'}s classification of periodic stable domains\/},Complex Variables Theory Appl. {\bf14} (1990), 211--214. MR 1048721
- *
- {Ste92}\bysame, {\em Rational iteration},Walter de Gruyter, Berlin,1993. MR 1224235
- *
- {Sul82} D. Sullivan,{\em It\'eration des fonctions analytiques complexes\/},C. R. Acad. Sci. Paris S\'er. I Math. {\bf294}(1982), 301--303. MR 658395
- *
- {Sul85}\bysame, {\em Quasiconformal homeomorphisms and dynamics \rom{I}.Solution of the Fatou-Julia problem on wandering domains\/},Ann. of Math. (2) {\bf122} (1985), 401--418. MR 819553
- *
- {Sul83}\bysame, {\em Quasiconformal homeomorphisms and dynamics \rom{III}.Topological conjugacy classes of analytic endomorphisms\/},preprint IHES/M/83/1, Institut des Hautes Etudes Scientifiques, 1983. MR
- *
- {Sut92} S. Sutherland,{\em Finding roots of complex polynomials with Newton\rom{'}s method},Ph.D. thesis, Boston Univ., 1989. MR
- *
- {Toe39} H. T\"opfer,{\em \"Uber die Iteration der ganzen transzendenten Funktionen,insbesondere von $\sin z$ und $\cos z$\/},Math. Ann. {\bf117} (1939), 65--84. MR 1293
- *
- {Toe49}\bysame, {\em Komplexe Iterationsindizes ganzer und rationaler Funktionen\/},Math. Ann. {\bf121} (1949), 191--222. MR 31549
- *
- {Val23} G. Valiron, {\em Lectures on the general theoryof integral functions}, \'Edouard Privat, Toulouse, 1923. MR
- *
- {Yan91} C.-C. Yang and J.-H. Zheng,{\em Further results on fixpoints and zeros of entire functions\/},Trans. Amer. Math. Soc. (to appear). MR 1179403
- *
- {Ye92} Zhuan Ye,{\em Structural instability of exponential functions\/},preprint. MR 1242788
- *
- {Yoc87} J.-C. Yoccoz,{\em Th\'eor\`eme de Siegel,nombres de Brjunoetpolyn\^omes quadratiques\/},preprint, 1987. MR
- *
- {Yoc88}\bysame, {\em Lin\'earisation des germes de diff\'eomorphismes holomorphesde $(C,0)$\/},C. R. Acad. Sci. Paris S\'er. I Math. {\bf306} (1988), 55--58. MR 929279
- *
- {Zho89} J. Zhou and Z. Li,{\em Structural instability of the mapping$z\to\lambda \exp(z) (\lambda>e^{-1})$\/},Sci. China Ser. A {\bf30} (1989), 1153--1161. MR 1057994
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(2000):
30D05, 58F08, 30D30, 65H05
Retrieve articles in all Journals with MSC
(2000):
30D05, 58F08, 30D30, 65H05
Additional Information:
DOI:
10.1090/S0273-0979-1993-00432-4
PII:
S 0273-0979(1993)00432-4
|