Dissipative homoclinic loops of two‐dimensional maps and strange attractors with one direction of instability |
| |
Authors: | Qiudong Wang William Ott |
| |
Affiliation: | 1. University of Arizona Department of Mathematics 617 N. Santa Rita Avenue P.O. Box 210089 Tucson, AZ 85721‐0089;2. University of Houston Department of Mathematics 651 PGH Houston, TX 77204‐3008 |
| |
Abstract: | We prove that when subjected to periodic forcing of the form certain two‐dimensional vector fields with dissipative homoclinic loops generate strange attractors with Sinai‐Ruelle‐Bowen measures for a set of forcing parameters (μ, ρ, ω) of positive Lebesgue measure. The proof extends ideas of Afraimovich and Shilnikov and applies the recent theory of rank 1 maps developed by Wang and Young. We prove a general theorem and then apply this theorem to an explicit model: a forced Duffing equation of the form © 2011 Wiley Periodicals, Inc. |
| |
Keywords: | |
|
|