Skip to main content
Log in

Horospheres and iterates of holomorphic maps

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Abate, M.: Boundary behavior of invariant distances and complex geodesics. Atti Accad. Naz. Lincei, VIII Ser., Rend., Cl. Sci. Fis. Mat. Nat.80, 100–106 (1986)

    Google Scholar 

  2. Bedford, E.: On the automorphism group of a Stein manifold. Math. Ann.266, 215–227 (1983)

    Google Scholar 

  3. Burckel, R.B.: Iterating self-maps of the disk. Am. Math. Mon.88, 396–407 (1981)

    Google Scholar 

  4. Chen, G.N.: Iteration of holomorphic maps of the open unit ball and the generalized upper half plane ofC n. J. Math. Anal. Appl.98, 305–313 (1984)

    Google Scholar 

  5. Denjoy, A.: Sur l'itération des fonctions analytiques. C.R. Acad. Sci. Paris182, 255–257 (1926)

    Google Scholar 

  6. Eustice, D.J.: Holomorphic idempotents and common fixed points on the 2-disk. Mich. Math. J.19, 347–352 (1972)

    Google Scholar 

  7. Earle, C.J., Hamilton, R.S.: A fixed point theorem for holomorphic mappings. In Proceedings of Symposia in Pure Mathematics, Vol. 16, pp. 61–65, Am. Math. Soc., Providence, 1969

    Google Scholar 

  8. Heins, M.H.: On the iteration of functions which are analytic and single-valued in a given multiply-connected region. Am. J. Math.63, 461–480 (1941)

    Google Scholar 

  9. Hervé, M.: Several complex variables, local theory, London: Oxford Univ. Press, 1963

    Google Scholar 

  10. Kubota, Y.: Iteration of holomorphic maps of the unit ball into itself. Proc. Am. Math. Soc.88, 476–480 (1983)

    Google Scholar 

  11. Lempert, L.: La métrique de Kobayashi et la réprésentation des domaines sur la boule. Bull. Soc. Math. Fr.109, 427–474 (1981)

    Google Scholar 

  12. MacCluer, B.D.: Iterates of holomorphic self-maps of the unit ball inC N. Mich. Math. J.30, 97–106 (1983)

    Google Scholar 

  13. Rudin, W.: Function theory on the unit ball ofC n. Berlin-Heidelberg-New York: Springer 1980

    Google Scholar 

  14. Shields, A.L.: On fixed points of commuting analytic functions. Proc. Am. Math. Soc.15, 703–706 (1964)

    Google Scholar 

  15. Stachura, A.: Iterates of holomorphic self-maps of the unit ball in Hilbert spaces. Proc. Am. Math. Soc.93, 88–90 (1985)

    Google Scholar 

  16. Suffridge, T.J.: Common fixed points of commuting holomorphic maps of the hyperball. Mich. Math. J.21, 309–314 (1974)

    Google Scholar 

  17. Vesentini, E.: Iteration of holomorphic maps. Russ. Math. Surv.40, 7–11 (1985)

    Google Scholar 

  18. Vigué, J.P.: Point fixes d'applications holomorphes dans un domaine borné convexe deC n. Trans. Am. Math. Soc.289, 345–353 (1985)

    Google Scholar 

  19. Vormoor, N.: Topologische Fortsetzung Biholomorphen Funktionen auf dem Rande bei Beschränkten Streng-pseudoconvexen Gebieten inC n mitC -rand. Math. Ann.204, 239–261 (1973)

    Google Scholar 

  20. Wolff, J.: Sur l'itération des fonctions holomorphes dans une région, et dont les valeurs appartiennent à cette région. C.R. Acad. Sci. Paris182, 42–43 (1926)

    Google Scholar 

  21. Wolff, J.: Sur l'itération des fonctions bornées. C.R. Acad. Sci. Paris182, 200–201 (1926)

    Google Scholar 

  22. Wolff, J.: Sur une généralisation d'un théoreme de Schwarz. C.R. Acad. Sci. Paris182, 918–920 (1926)

    Google Scholar 

  23. Wu, H.: Normal families of holomorphic mappings. Acta Math.119, 193–233 (1967)

    Google Scholar 

  24. Yang, P.: Holomorphic curves and boundary regularity of biholomorphic maps of pseudoconvex domains. Preprint, 1978

Download references

Author information

Authors and Affiliations

Authors

Additional information

This paper was written while the author was visiting the University of California Berkeley

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abate, M. Horospheres and iterates of holomorphic maps. Math Z 198, 225–238 (1988). https://doi.org/10.1007/BF01163293

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01163293

Navigation