Dissipative homoclinic loops and rank one chaos
Abstract
We prove that when subjected to periodic forcing of the form pμ, , (t) = μ ( h(x,y) + ( 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, , ) 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 H\'enon maps by Benedicks and Carleson.
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