Dissipative homoclinic loops and rank one chaos
Abstract
Description
We prove that when subjected to periodic forcing of the form $p_{μ, \rh, \om} (t) = μ(\rh h(x,y) + \sin (\om t))$, certain second order systems of differential equations with dissipative homoclinic loops admit strange attractors with SRB measures for a set of forcing parameters $(μ, \rh, \om)$ of positive measure. Our proof applies the recent theory of rank one maps, developed by Wang and Young based on the analysis of strongly dissipative Hénon maps by Benedicks and Carleson.