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arXiv · 0802.4283

Dissipative homoclinic loops and rank one chaos

Qiudong Wang·William Ott
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Abstract

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.

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Qiudong Wang, William Ott. 2008-02-29. Dissipative homoclinic loops and rank one chaos. https://arxiv.org/abs/0802.4283

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