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On the finiteness of attractors for piecewise $C^{2}$ maps of the interval

  • P. BRANDÃO (a1), J. PALIS (a1) and V. PINHEIRO (a2)

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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On the finiteness of attractors for piecewise $C^{2}$ maps of the interval

  • P. BRANDÃO (a1), J. PALIS (a1) and V. PINHEIRO (a2)

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