Article ID Journal Published Year Pages File Type
5500383 Physica D: Nonlinear Phenomena 2016 17 Pages PDF
Abstract
Horseshoes play a central role in dynamical systems and are observed in many chaotic systems. However most points in a neighborhood of the horseshoe escape after finitely many iterations. In this work we construct a new model by re-injecting the points that escape the horseshoe. We show that this model can be realized within an attractor of a flow arising from a three-dimensional vector field, after perturbation of an inclination-flip homoclinic orbit with a resonance. The dynamics of this model, without considering the re-injection, often contains a cuspidal horseshoe with positive entropy, and we show that for a computational example the dynamics with re-injection can have more complexity than the cuspidal horseshoe alone.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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