Dissipative homoclinic loops and rank one chaos

Details Dissipative homoclinic loops and rank one chaos Dissipative homoclinic loops and rank one chaos

2008-02-28

arxiv.org/abs/0802.4283v2

Mathematics

Dynamical Systems

Scientific paper

We prove that when subjected to periodic forcing of the form $p_{\mu, \rh, \om} (t) = \mu (\rh h(x,y) + \sin (\om t))$, certain second order systems of differential equations with dissipative homoclinic loops admit strange attractors with SRB measures for a set of forcing parameters $(\mu, \rh, \om)$ 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 H\'enon maps by Benedicks and Carleson.

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