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On the C2-creation of links of critical points

Published online by Cambridge University Press:  19 September 2008

Gonzalo Contreras
Gonzalo Contreras
Affiliation:
Dpto. de Matemática, PUC-Rio, R. Marquês de São Vicente 225, 22453 Rio de Janeiro, Brasil.
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Abstract

We give necessary conditions for an endomorphism of the interval not to be C2+α-approximated by endomorphisms having a link between critical points. We apply these techniques to show that on a C2+α-generic set of unimodal maps the endomorphisms are either Axiom A or there exists an ergodic measure with zero Lyapunov exponent. Applying this result we prove the formula conjectured by Eckmann and Ruelle for the rate of escape of the complement of the basin of the sinks. We add some remarks on the C2-stability conjecture.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 2 , June 1993 , pp. 263 - 288
Copyright
Copyright © Cambridge University Press 1993

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References

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