arXiv subjects

B. Pires

Publications and source records attributed to B. Pires.

4 recordsLinked to original sources

arXiv2018

Li-Yorke Chaos for Composition Operators on $L^p$-Spaces

Li-Yorke chaos is a popular and well-studied notion of chaos. Several simple and useful characterizations of this notion of chaos in the setting of linear dynamics were obtained recently. In this note we show that even simpler and more useful characterizations of Li-Yorke chaos can be given in the special setting of composition operators on $L^p$ spaces. As a consequence we obtain a simple characterization of weighted shifts which are Li-Yorke chaotic. We give numerous examples to show that our results are sharp.

math.DS↗

arXiv2008

Unique ergodicity of circle and interval exchange transformations with flips

We study the existence of transitive exchange maps with flips defined on the unit circle. We provide a complete answer to the question of whether there exists a transitive exchange map of the unit circle defined on n subintervals and having f flips.

math.DS↗

arXiv2008

Affine interval exchange transformations with flips and wandering intervals

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips having wandering intervals and such that the support of the invariant measure is a Cantor set.

math.DS↗

arXiv2006

Asymptotic stability at infinity for differentiable vector fields of the plane

Let X:R2\Dr->R2 be a differentiable (but not necessarily C1) vector field, where r>0 and Dr={z\in R2:|z|\le r}. If for some e>0 and for all p\in R2\Dr, no eigenvalue of D_p X belongs to (-e,0]\cup {z\in\C:\mathcal{R}(z)\ge 0}, then (a)For all p\in R2\Dr, there is a unique positive semi--trajectory of X starting at p; (b)\mathcal{I}(X), the index of X at infinity, is a well defined number of the extended real line [-\infty,\infty); (c) There exists a constant vector v\in R2 such that if \mathcal{I}(X) is less than zero (resp. greater or equal to zero), then the point at infinity \infty of the Riemann sphere R2\cup\set{\infty} is a repellor (resp. an attractor) of the vector field X+v.

math.DS↗