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Quantitative recurrence for generic homeomorphisms

Author: André Junqueira
Journal: Proc. Amer. Math. Soc. 145 (2017), 4751-4761
MSC (2010): Primary 37B20, 37E30, 37C20; Secondary 37A25
Published electronically: July 27, 2017
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Abstract: In this article we study quantitative recurrence for generic measure preserving homeomorphisms on euclidian spaces with respect to Lebesgue measure and compact manifolds with respect to Oxtoby-Ulam measures (i.e., it is nonatomic and positive on each open set). As an application we show that the decay of correlations of generic measure preserving homeomorphisms on compact manifolds is slow.

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Additional Information

André Junqueira
Affiliation: Departamento de Matemática, Universidade Federal de Viçosa, Campus Universitário, CEP 36570-900, Viçosa, MG, Brazil

Keywords: Recurrence, generic properties, periodic points.
Received by editor(s): May 9, 2015
Received by editor(s) in revised form: August 8, 2016
Published electronically: July 27, 2017
Additional Notes: This research was partially supported by Capes from Brazil
Communicated by: Yingfei Yi
Article copyright: © Copyright 2017 American Mathematical Society

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