A  reinjected cuspidal horseshoe

Marcus Fontaine; William D. Kalies; Vincent Naudot

doi:10.3934/proc.2013.2013.227

Article Contents

2013, Volume 2013: 227-236. Doi: 10.3934/proc.2013.2013.227 open access

This issue Previous Article The role of lower and upper solutions in the generalization of Lidstone problems Next Article Abstract theory of variational inequalities and Lagrange multipliers

A reinjected cuspidal horseshoe

1.
Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, 33431 Boca Raton

Received: August 31, 2012

Revised: June 30, 2013

Published: October 2013

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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.

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Mathematics Subject Classification: Primary: 37D45, 37C29; Secondary: 37B10.

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