Central Lyapunov exponent of partially hyperbolic diffeomorphisms of \mathbbT³

2012/04/04 by Ponce, Gabriel, Tahzibi, Ali
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1204.0994

Abstract

In this paper we construct some "pathological" volume preserving partially hyperbolic diffeomorphisms on \toro3 such that their behaviour in small scales in the central direction (Lyapunov exponent) is opposite to the behavior of their linearization. These examples are isotopic to Anosov. We also get partially hyperbolic diffeomorphisms isotopic to Anosov (consequently with non-compact central leaves) with zero central Lyapunov exponent at almost every point.

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