Generalized Hénon-Devaney maps

Lundi 22 octobre 2018 10:15-11:45 - Fernando Lenarduzzi - UFSCar, São Carlos, Brésil

Résumé : We shall consider the two-parameter family f_a,b of self-maps of R^2 given by (x,y) → (ax+1/y, by-b/y-abx) where 0<a≤b≤1. When a=b=1 this map is known as the « Hénon-Devaney map ». We will give some dynamical and ergodic properties of these maps.
For all the parameters, we exhibit two transversal invariant C^1 foliations. For a<b, there is a global unbounded transitive attractor exhibiting a type of SRB measure. If b=1 the measure is infinite, and if b<1 the measure is finite. Moreover, in the last case the attractor is robustly transitive and stable in the sense that for nearby systems there is a conjugated attractor. For the Hénon-Devaney map (a=b=1), we get a conjugation to a subshift, providing a global understanding of the map’s behavior.

Lieu : salle 3L8

Generalized Hénon-Devaney maps  Version PDF