Richness of Chaos in the absolute newhouse domain

Dmitry Turaev

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

17 Scopus citations

Abstract

We show that universal maps (i.e. such whose iterations approximate every possible dynamics arbitrarily well) form a residual subset in an open set in the space of smooth dynamical systems. The result implies that many dynamical systems emerging in natural applications may, on a very long time scale, have quite unexpected dynamical properties, like coexistence of many non-trivial hyperbolic attractors and repellers and attractors with all zero Lyapunov exponents. Applications to reversible and symplectic maps are also considered.

Original languageEnglish
Title of host publicationProceedings of the International Congress of Mathematicians 2010, ICM 2010
Pages1804-1815
Number of pages12
StatePublished - 1 Dec 2010
Externally publishedYes
EventInternational Congress of Mathematicians 2010, ICM 2010 - Hyderabad, India
Duration: 19 Aug 201027 Aug 2010

Publication series

NameProceedings of the International Congress of Mathematicians 2010, ICM 2010

Conference

ConferenceInternational Congress of Mathematicians 2010, ICM 2010
Country/TerritoryIndia
CityHyderabad
Period19/08/1027/08/10

Keywords

  • Elliptic orbit
  • Hamiltonian system
  • Homoclinic tangency
  • Hyperbolic attrac-tor
  • Renormalization
  • Reversible system
  • Zero Lyapunov exponent

ASJC Scopus subject areas

  • General Mathematics

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