arXiv subjects

Cesar Silva

Publications and source records attributed to Cesar Silva.

2 recordsLinked to original sources

arXiv2017

Infinite symmetric ergodic index and related examples in infinite measure

We define an infinite measure-preserving transformation to have infinite symmetric ergodic index if all finite Cartesian products of the transformation and its inverse are ergodic, and show that infinite symmetric ergodic index does not imply that all products of powers are conservative, so does not imply power weak mixing. We provide a sufficient condition for $k$-fold and infinite symmetric ergodic index and use it to answer a question on the relationship between product conservativity and product ergodicity. We also show that a class of rank-one transformations that have infinite symmetric ergodic index are not power weakly mixing, and precisely characterize a class of power weak transformations that generalizes existing examples.

math.DS↗

arXiv2010

Dense area-preserving homeomorphisms have zero Lyapunov exponents

We give a new definition for a Lyapunov exponent (called new Lyapunov exponent) associated to a continuous map. Our first result states that these new exponents coincide with the usual Lyapunov exponents if the map is differentiable. Then, we apply this concept to prove that there exists a C0-dense subset of the set of the area-preserving homeomorphisms defined in a compact, connected and boundaryless surface such that any element inside this residual subset has zero new Lyapunov exponents for Lebesgue almost every point. Finally, we prove that the function that associates an area-preserving homeomorphism, equipped with the C0-topology, to the integral (with respect to area) of its top new Lyapunov exponent over the whole surface cannot be upper-semicontinuous.

math.DS↗