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arXiv · 1506.00276

On the Finiteness of Attractors for piecewise $C^2$ Maps of the Interval

Paulo Brandão·Jacob Palis·Vilton Pinheiro
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Abstract

We consider piecewise $C^2$ non-flat maps of the interval and show that, for Lebesgue almost every point, its omega-limit set is either a periodic orbit, a cycle of intervals or the closure of the orbits of a subset of the critical points. In particular, every piecewise $C^2$ non-flat map of the interval displays only a finite number of non-periodic attractors.

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Paulo Brandão, Jacob Palis, Vilton Pinheiro. 2015-05-31. On the Finiteness of Attractors for piecewise $C^2$ Maps of the Interval. https://arxiv.org/abs/1506.00276

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