Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(e) ISSN 0894-0347(p)

     

The Fibonacci unimodal map

Author(s): Mikhail Lyubich; John Milnor
Journal: J. Amer. Math. Soc. 6 (1993), 425-457.
MSC: Primary 58F08; Secondary 26A18, 30D05, 39B12, 58F03
MathSciNet review: 1182670
Retrieve article in: PDF
This article is available free of charge

References | Similar articles | Additional information

References:

[BD]
B. Branner and A. Douady, Surgery on complex polynomials, preprint, Matematic Institut, Denmark, 1987-05. MR 980952 (90e:58114)

[BH]
B. Branner and J. H. Hubbard, The iteration of cubic polynomials, Part II: patterns and parapatterns, Acta Math. (to appear).

[BL1]
A. Blokh and and M. Lyubich, Non-existence of wandering intervals and structure of topological attractors for one dimensional dynamical systems, Ergodic Theory Dynamical Systems 9 (1989), 751-758. MR 1036906 (91e:58101)

[BL2]
-, Measurable dynamics of $             S$-unimodal maps of the interval, Ann. Sci. Ecole Norm. Sup. (4) 24 (1991), 545-573. MR 1132757 (93f:58132)

[BL3]
-, Measure and dimension of solenoidal attractors of one-dimensional dynamical systems, Comm. Math. Phys. 127 (1990), 573-583. MR 1040895 (91g:58164)

[DH]
A. Douady and J. H. Hubbard, On the dynamics of polynomial-like maps, Ann. Sci. Ecole Norm. Sup. (4) 18 (1985), 287-343. MR 816367 (87f:58083)

[G1]
J. Guckenheimer, Sensitive dependence to initial conditions for one-dimensional maps, Comm. Math. Phys. 70 (1979), 133-160. MR 553966 (82c:58037)

[G2]
-, Limit sets of $ S$-unimodal maps with zero entropy, Comm. Math. Phys. 110, 655-659. MR 895222 (88i:58111)

[H]
J. H. Hubbard, according to J.-C. Yoccoz, Puzzles and quadratic tableaux, preprint, 1990.

[HK]
F. Hofbauer and G. Keller, Some remarks on recent results about $ S$-unimodal maps, Ann. Inst. H. Poincaré Phys. Théor. 53 (1990), 413-425. MR 1096100 (92m:58077)

[L1]
M. Lyubich, Non-existence of wandering intervals and structure of topological attractors for one dimensional dynamical systems, Ergodic Theory Dynamical Systems 9 (1989), 737-750. MR 1036905 (91e:58100)

[L2]
-, On the Lebesgue measure of the Julia set of a quadratic polynomial, preprint, IMS, 1991/10.

[KP]
J. Ketoja and O. Piirila, On the abnormality of the period doubling bifurcation, Phys. Lett. A 138 (1989), 488-492. MR 1007786 (91c:58094)

[M]
J. Milnor, On the concept of attractor, Comm. Math. Phys. 99 (1985), 177-195; 102 (1985), 517-519. MR 790735 (87i:58109a)

[MT]
J. Milnor and W. Thurston, On iterated maps of the interval, Dynamical Systems, Proc. U. Md., 1986-87, (J. Alexander, ed.), Lecture Notes in Math., vol. 1342, Springer, New York, 1988, pp. 465-563. MR 970571 (90a:58083)

[Ma]
M. Martens, Cantor attractors of unimodal maps, Thesis, 1990.

[MvS]
W. de Melo and S. van Strien, A structure theorem in one-dimensional dynamics, Ann. of Math. (2) 129 (1989), 519-546. MR 997312 (90m:58106)

[NvS]
T. Nowicki and S. van Strien, Invariant measures exist under a summability condition for unimodal maps, Invent. Math. 105 (1991), 123-136. MR 1109621 (93b:58094)

[PTT]
I. Procaccia, S. Thomae, and C. Tresser, First return maps as a unified renormalization scheme for dynamical systems, Phys. Rev. A 35 (1987), 1884-1900. MR 879250 (88f:58111)

[S]
D. Sullivan, Bounds, quadratic differentials, and renormalization conjectures, preprint, 1990. MR 1184622 (93k:58194)

[Sh]
K. Shibayama, Fibonacci sequence of stable periodic orbits for one-parameter families of $             {C^1}$-unimodal mappings, preprint. MR 797605 (86m:58132)

[Sw1]
G. Swiatek, Rational rotation numbers for maps of the circle, Comm. Math. Phys. 119 (1988), 109-128. MR 968483 (90h:58077)

[Sw2]
-, Bounded distortion properties of one-dimensional maps, preprint, SUNY, Stony Brook, 1990/10.

[T]
I. Tsuda, On the abnormality of period doubling bifurcations, Progress Theor. Phys. 66 (1985), 1985-2002. MR 647442 (83m:58054)

[TV]
F. Tangerman and P. Veerman, Scaling in circle maps. I, Comm. Math. Phys. 134 (1990), 89-107. MR 1079802 (92h:58106)

[VL]
A. M. Vershik and A. M. Livshitz, Adic models of ergodic transformations, preprint, University of California, Berkeley, PAM-499 (1990).

[Y1]
J.-C. Yoccoz, Il n'y a pas de contre-exemple de Denjoy analytiques, C. R. Acad. Sci. Paris Ser. I. Math. 289 (1984), 141-144. MR 741080 (85j:58134)

[Y2]
-, Manuscript, 1990.

Similar Articles:

Retrieve articles in Journal of the American Mathematical Society with MSC: 58F08, 26A18, 30D05, 39B12, 58F03

Retrieve articles in all Journals with MSC: 58F08, 26A18, 30D05, 39B12, 58F03


Additional Information:

DOI: 10.1090/S0894-0347-1993-1182670-0
PII: S0894-0347-1993-1182670-0
Copyright of article: Copyright 1993, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia