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Closing lemma for holomorphic functions in ${\Bbb C}$

Published online by Cambridge University Press:  01 February 1998

JOHN ERIK FORNÆSS  and
NESSIM SIBONY
JOHN ERIK FORNÆSS
Affiliation:
Mathematics Department, University of Michigan, Ann Arbor, Michigan 48109, USA
NESSIM SIBONY
Affiliation:
Universite Paris Sud, URA757, Bat 425. Mathematiques, 91405 Orsay, France
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Abstract

Let $F_\lambda(z)= \lambda z + {\cal O}(z^2)$ be a one parameter holomorphic family of holomorphic maps defined in a neighborhood of $\lambda_0* \overline{\mbox{D}}$. Assume that $F_{\lambda_0}$ has a Siegel disc $\Delta_0$, then the orbit of a point in the interior of the Siegel disc can be followed very closely by periodic orbits of nearby maps. The same technique is applied to Herman rings and Cremer points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 1 , February 1998 , pp. 153 - 170
Copyright
1998 Cambridge University Press

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