Real bounds and Lyapunov exponents
Edson de Faria Pablo Guarino
We prove that a $C^3$ critical circle map without periodic points has zero Lyapunov exponent with respect to its unique invariant Borel probability measure. Moreover, no critical point of such a map satisfies the Collet-Eckmann condition. This result is proved directly from the well-known real a-priori bounds, without using Pesin's theory. We also show how our methods yield an analogous result for infinitely renormalizable unimodal maps of any combinatorial type. Finally we discuss an application of these facts to the study of neutral measures of certain rational maps of the Riemann sphere.
keywords: real bounds Lyapunov exponents infinitely renormalizable unimodal maps critical circle maps neutral measures on Julia sets.

Year of publication

Related Authors

Related Keywords

[Back to Top]