Transitivity and Topological Mixing for $${C}^{1}$$ Diffeomorphisms

Flavio Abdenur () and Sylvain Crovisier ()
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Flavio Abdenur: Ventor Investimentos
Sylvain Crovisier: Université Paris-Sud 11, Département de Mathématiques, UMR 8628

A chapter in Essays in Mathematics and its Applications, 2012, pp 1-16 from Springer

Abstract: Abstract We prove that, on connected compact manifolds, both C 1-generic conservative diffeomorphisms and C 1-generic transitive diffeomorphisms are topologically mixing. This is obtained through a description of the periods of a homoclinic class and by a control of the period of the periodic points given by the closing lemma.

Keywords: Periodic Orbit; Periodic Point; Closing Lemma; Homoclinic Class; Hyperbolic Periodic Orbit (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-28821-0_1

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DOI: 10.1007/978-3-642-28821-0_1

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