Quantitative recurrence for generic homeomorphisms
HTML articles powered by AMS MathViewer
- by André Junqueira PDF
- Proc. Amer. Math. Soc. 145 (2017), 4751-4761 Request permission
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.References
- Jon Aaronson, An introduction to infinite ergodic theory, Mathematical Surveys and Monographs, vol. 50, American Mathematical Society, Providence, RI, 1997. MR 1450400, DOI 10.1090/surv/050
- Steve Alpern and V. S. Prasad, Typical dynamics of volume preserving homeomorphisms, Cambridge Tracts in Mathematics, vol. 139, Cambridge University Press, Cambridge, 2000. MR 1826331
- Claudio Bonanno, Stefano Galatolo, and Stefano Isola, Recurrence and algorithmic information, Nonlinearity 17 (2004), no. 3, 1057–1074. MR 2057140, DOI 10.1088/0951-7715/17/3/016
- Michael D. Boshernitzan, Quantitative recurrence results, Invent. Math. 113 (1993), no. 3, 617–631. MR 1231839, DOI 10.1007/BF01244320
- Fons Daalderop and Robbert Fokkink, Chaotic homeomorphisms are generic, Topology Appl. 102 (2000), no. 3, 297–302. MR 1745449, DOI 10.1016/S0166-8641(98)00155-2
- Stefano Galatolo, Dimension via waiting time and recurrence, Math. Res. Lett. 12 (2005), no. 2-3, 377–386. MR 2150891, DOI 10.4310/MRL.2005.v12.n3.a8
- Stefano Galatolo and Dong Han Kim, The dynamical Borel-Cantelli lemma and the waiting time problems, Indag. Math. (N.S.) 18 (2007), no. 3, 421–434. MR 2373690, DOI 10.1016/S0019-3577(07)80031-0
- James R. Munkres, Topology: a first course, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1975. MR 0464128
- Jérôme Rousseau, Recurrence rates for observations of flows, Ergodic Theory Dynam. Systems 32 (2012), no. 5, 1727–1751. MR 2974217, DOI 10.1017/S014338571100037X
- Jérôme Rousseau and Benoît Saussol, Poincaré recurrence for observations, Trans. Amer. Math. Soc. 362 (2010), no. 11, 5845–5859. MR 2661498, DOI 10.1090/S0002-9947-2010-05078-0
- Peter Walters, An introduction to ergodic theory, Graduate Texts in Mathematics, vol. 79, Springer-Verlag, New York-Berlin, 1982. MR 648108
Additional Information
- André Junqueira
- Affiliation: Departamento de Matemática, Universidade Federal de Viçosa, Campus Universitário, CEP 36570-900, Viçosa, MG, Brazil
- MR Author ID: 1053538
- Email: andre.junqueira@ufv.br, andrejunqueiracorrea@gmail.com
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4751-4761
- MSC (2010): Primary 37B20, 37E30, 37C20; Secondary 37A25
- DOI: https://doi.org/10.1090/proc/13430
- MathSciNet review: 3691992