Weak mixing and product recurrence

Piotr Oprocha[1]

  • [1] Universidad de Murcia Departamento de Matemáticas Campus de Espinardo 30100 Murcia (Spain) AGH University of Science and Technology Faculty of Applied Mathematics al. Mickiewicza 30 30-059 Kraków (Poland)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 4, page 1233-1257
  • ISSN: 0373-0956

Abstract

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In this article we study the structure of the set of weakly product recurrent points. Among others, we provide necessary conditions (related to topological weak mixing) which imply that the set of weakly product recurrent points is residual. Additionally, some new results about the class of systems disjoint from every minimal system are obtained.

How to cite

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Oprocha, Piotr. "Weak mixing and product recurrence." Annales de l’institut Fourier 60.4 (2010): 1233-1257. <http://eudml.org/doc/116302>.

@article{Oprocha2010,
abstract = {In this article we study the structure of the set of weakly product recurrent points. Among others, we provide necessary conditions (related to topological weak mixing) which imply that the set of weakly product recurrent points is residual. Additionally, some new results about the class of systems disjoint from every minimal system are obtained.},
affiliation = {Universidad de Murcia Departamento de Matemáticas Campus de Espinardo 30100 Murcia (Spain) AGH University of Science and Technology Faculty of Applied Mathematics al. Mickiewicza 30 30-059 Kraków (Poland)},
author = {Oprocha, Piotr},
journal = {Annales de l’institut Fourier},
keywords = {Product recurrence; weak mixing; minimal system; disjointness; product recurrence},
language = {eng},
number = {4},
pages = {1233-1257},
publisher = {Association des Annales de l’institut Fourier},
title = {Weak mixing and product recurrence},
url = {http://eudml.org/doc/116302},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Oprocha, Piotr
TI - Weak mixing and product recurrence
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 4
SP - 1233
EP - 1257
AB - In this article we study the structure of the set of weakly product recurrent points. Among others, we provide necessary conditions (related to topological weak mixing) which imply that the set of weakly product recurrent points is residual. Additionally, some new results about the class of systems disjoint from every minimal system are obtained.
LA - eng
KW - Product recurrence; weak mixing; minimal system; disjointness; product recurrence
UR - http://eudml.org/doc/116302
ER -

References

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  6. Tomasz Downarowicz, Jacek Serafin, Semicocycle extensions and the stroboscopic property, Topology Appl. 153 (2005), 97-106 Zbl1076.37007MR2172037
  7. H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Systems Theory 1 (1967), 1-49 Zbl0146.28502MR213508
  8. H. Furstenberg, Recurrence in ergodic theory and combinatorial number theory, (1981), Princeton University Press, Princeton, N.J. Zbl0459.28023MR603625
  9. Juan Luis García Guirao, Dominik Kwietniak, Marek Lampart, Piotr Oprocha, Alfredo Peris, Chaos on hyperspaces, Nonlinear Anal. 71 (2009), 1-8 Zbl1175.37024MR2518006
  10. Kamel Haddad, William Ott, Recurrence in pairs, Ergodic Theory Dynam. Systems 28 (2008), 1135-1143 Zbl1162.37005MR2437223
  11. Wen Huang, Xiangdong Ye, Dynamical systems disjoint from any minimal system, Trans. Amer. Math. Soc. 357 (2005), 669-694 Zbl1072.37011MR2095626
  12. Héctor Méndez, On density of periodic points for induced hyperspace maps, Top. Proc. 35 (2010), 281-290 Zbl1177.54019MR2545027
  13. Piotr Oprocha, Spectral decomposition theorem for non-hyperbolic maps, Dyn. Syst. 23 (2008), 299-307 Zbl1153.37334MR2455262
  14. S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817 Zbl0202.55202MR228014

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