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arXiv · 1703.03964

Renormalization of two-dimensional piecewise linear maps: Abundance of 2-D strange attractors

Antonio Pumariño·José Ángel Rodríguez·Enrique Vigil
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Abstract

For a two parameter family of two-dimensional piecewise linear maps and for every natural number $ n $ we prove not only the existence of intervals of parameters for which the respective maps are $ n $ times renormalizable but also we show the existence of intervals of parameters where the coexistence of at least $ 2^n $ strange attractors takes place. This family of maps contains the two-dimensional extension of the classical one-dimensional family of tent maps.

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Antonio Pumariño, José Ángel Rodríguez, Enrique Vigil. 2017-03-11. Renormalization of two-dimensional piecewise linear maps: Abundance of 2-D strange attractors. https://arxiv.org/abs/1703.03964

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