arXiv subjects

José Santana Costa

Publications and source records attributed to José Santana Costa.

2 recordsLinked to original sources

arXiv2024

Rigidity of Lyapunov exponents for derived from Anosov diffeomorphisms

For a class of volume preserving partially hyperbolic diffeomorphisms (or non-uniformly Anosov) $f\colon {\T}^d\rightarrow{\T}^d$ homotopic to linear Anosov automorphism, we show that the sum of the positive (negative) Lyapunov exponents of $f$ is bounded above (resp. below) by the sum of the positive (resp. negative) Lyapunov exponents of its linearization. We show this for some classes of derived from Anosov (DA) and non-uniformly hyperbolic systems with dominated splitting, in particular for examples described by C. Bonatti and Viana. The results in this paper address a flexibility program by J. Bochi, A. Katok and F. Rodriguez Hertz.

math.DS↗

arXiv2023

On Lyapunov exponents properties of special Anosov endomorphisms on $\mathbb{T}^d$

This work is addressed to study Anosov endomorphisms of $\mathbb{T}^d,$ $d\geq 3.$ We are interested to obtain metric and topological information on such Anosov endomorphism by comparison between their Lyapunov exponents and the ones of its linearization. We can characterize when a weak unstable foliation of a special Anosov endomorphism near to linear is an absolutely continuous foliation. Also, we show that in dimension $d \geq 3,$ it is possible to find a smooth special Anosov endomorphism being conservative but not Lipschitz conjugate with its linearization, in contrast with the smooth rigidity in dimension two.

math.DS↗