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A reinjected cuspidal horseshoe

Pages: 227 - 236, Issue special, November 2013

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Marcus Fontaine - Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, 33431 Boca Raton, United States (email)
William D. Kalies - Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, 33431 Boca Raton, United States (email)
Vincent Naudot - Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, 33431 Boca Raton, United States (email)

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 finite iterations. In this work we construct a model that possesses an attracting set that contains a cuspidal horseshoe with positive entropy. This model is obtained by reinjecting the points that escape the horseshoe and can be realized in a 3-dimensional vector field.

Keywords:  Cuspidal horseshoe, inclination-flip homoclinic orbit, PoincarĂ© return map, hyperbolicity, topological entropy, invariant foliation.
Mathematics Subject Classification:  Primary: 37D45, 37C29; Secondary: 37B10.

Received: September 2012;      Revised: July 2013;      Published: November 2013.

 References