arXiv subjects

William Ott

Publications and source records attributed to William Ott.

20 records · Page 2Linked to original sources

arXiv2008

Dissipative homoclinic loops and rank one chaos

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.

math.DS↗

arXiv2007

Strange attractors in periodically-kicked degenerate Hopf bifurcations

We prove that spiral sinks (stable foci of vector fields) can be transformed into strange attractors exhibiting sustained, observable chaos if subjected to periodic pulsatile forcing. We show that this phenomenon occurs in the context of periodically-kicked degenerate supercritical Hopf bifurcations. The results and their proofs make use of a new multi-parameter version of the theory of rank one maps developed by Wang and Young.

math.DS↗