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A reinjected cuspidal horseshoe

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

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