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

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

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...

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Veröffentlicht in:	arXiv.org 2016-03
Hauptverfasser:	Brandão, Paulo, Palis, Jacob, Pinheiro, Vilton
Format:	Artikel
Sprache:	eng
Schlagworte:	Critical point
Online-Zugang:	Volltext
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Zusammenfassung:	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.
ISSN:	2331-8422

Zusammenfassung:	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.
ISSN:	2331-8422

On the Finiteness of Attractors for piecewise \(C^2\) Maps of the Interval