Existence of robust non-uniformly hyperbolic endomorphism in homotopy classes

2023/01/05 by Janeiro, Victor
#37D25 37A05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.02180

Abstract

We extend the results of arXiv:2206.08295v2 by showing that any homothety in \mathbb T² is homotopic to a non-uniformly hyperbolic ergodic area preserving map, provided that its degree is at least 5². We also address other small topological degree cases not considered in the previous article. This proves the existence of a \mathcal C¹ open set of non-uniformly hyperbolic systems, that intersects essentially every homotopy classes in \mathbb T², where the Lyapunov exponents vary continuously.

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