Asymptotic expansion of smooth interval maps

Details Asymptotic expansion of smooth interval maps Asymptotic expansion of smooth interval maps

2012-04-13

arxiv.org/abs/1204.3071v1

Mathematics

Dynamical Systems

Scientific paper

We show that several different ways to quantify the asymptotic expansion of a non-degenerate smooth interval map coincide. A consequence is an extension to multimodal maps of the remarkable result of Nowicki and Sands giving several characterizations of the Collet-Eckmann condition for unimodal maps. Combined with a result of Nowicki and Przytycki, this implies that several natural non-uniform hyperbolicity conditions are invariant under topological conjugacy. Another consequence is for the thermodynamic formalism of non-degenerate smooth maps: A high-temperature phase transition occurs precisely when the Topological Collet-Eckmann condition fails.

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