arXiv subjects

Vilton Pinheiro

Publications and source records attributed to Vilton Pinheiro.

21 records · Page 2Linked to original sources

arXiv2006

Topological structure of (partially) hyperbolic sets with positive volume

We consider both hyperbolic sets and partially hyperbolic sets attracting a set of points with positive volume in a Riemannian manifold. We obtain several results on the topological structure of such sets for diffeomorphisms whose differentiability is bigger than one. We show in particular that there are no partially hyperbolic horseshoes with positive volume for such diffeomorphisms. We also give a description of the limit set of almost every point belonging to a hyperbolic set or a partially hyperbolic set with positive volume.

math.DS↗

arXiv2005

On the nonexistence of fat partially hyperbolic horseshoes

We show that there are no partially hyperbolic horseshoes with positive Lebesgue measure for diffeomorphisms whose class of differentiability is higher than 1. This generalizes a classical result by Bowen for uniformly hyperbolic horseshoes.

math.DS↗

arXiv2004

Backward volume contraction for endomorphisms with eventual volume expansion

We consider smooth maps on compact Riemannian manifolds. We prove that under some mild condition of eventual volume expansion Lebesgue almost everywhere we have uniform backward volume contraction on every pre-orbit for Lebesgue almost every point.

math.DS↗