On the Finiteness of Attractors for piecewise C² Maps of the Interval

2015/05/31 by P. A. Brandão, Brandão, Paulo, Jacob Palis +3
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1506.00276

openalex publication_date 2015/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider piecewise C² 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 C² non-flat map of the interval displays only a finite number of non-periodic attractors.

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