Journal of Modern Dynamics (JMD)

Critical points for surface diffeomorphisms

Pages: 615 - 648, Issue 4, October 2007      doi:10.3934/jmd.2007.1.615

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Enrique R. Pujals - IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brazil (email)
Federico Rodriguez Hertz - IMERL-Facultad de IngenierĂ­a, Universidad de la RepĂșblica, ulio Herrera y Reissig 565, CC 30, 11300 Montevideo, Uruguay (email)

Abstract: Using the definition of dominated splitting, we introduce the notion of critical set for any dissipative surface diffeomorphism as an intrinsically well-defined object. We obtain a series of results related to this concept.

Keywords:  smooth mappings and diffeomorphisms, homeomorphisms and diffeomorphisms of planes and surfaces, nonuniformly hyperbolic systems, partially hyperbolic systems, dominated splitting.
Mathematics Subject Classification:  Primary: 37C05, 37E30, 37D25, 37D30.

Received: February 2007;      Revised: August 2007;      Available Online: July 2007.