Measure theory and geometric topology in dynamics

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

In this survey we shall present some relations between measure theory and geometric topology in dynamics. One of these relations comes as follows, on one hand from topological information of the system, some structure should be preserved by the dynamics at least in some weak sense, on the other hand, measure theory is soft enough that an invariant geometric structure almost always appears along some carefully chosen invariant measure. As an example, we have the known result that in dimension 2 the system has asymptotic growth of hyperbolic periodic orbits at least equal to the largest exponent of the action in homology.

Original languageEnglish (US)
Title of host publicationProceedings of the International Congress of Mathematicians 2010, ICM 2010
Pages1760-1776
Number of pages17
StatePublished - Dec 1 2010
EventInternational Congress of Mathematicians 2010, ICM 2010 - Hyderabad, India
Duration: Aug 19 2010Aug 27 2010

Publication series

NameProceedings of the International Congress of Mathematicians 2010, ICM 2010

Other

OtherInternational Congress of Mathematicians 2010, ICM 2010
CountryIndia
CityHyderabad
Period8/19/108/27/10

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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    Rodriguez Hertz, F. J. (2010). Measure theory and geometric topology in dynamics. In Proceedings of the International Congress of Mathematicians 2010, ICM 2010 (pp. 1760-1776). (Proceedings of the International Congress of Mathematicians 2010, ICM 2010).