Critical points for surface diffeomorphisms

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October 2007, 1(4): 615-648. doi: 10.3934/jmd.2007.1.615

Critical points for surface diffeomorphisms

Enrique R. Pujals ^1, and Federico Rodriguez Hertz ^2,

1.	IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brazil
2.	IMERL-Facultad de Ingeniería, Universidad de la República, ulio Herrera y Reissig 565, CC 30, 11300 Montevideo, Uruguay

Received February 2007 Revised August 2007 Published July 2007

Abstract
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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: partially hyperbolic systems, smooth mappings and diffeomorphisms, homeomorphisms and diffeomorphisms of planes and surfaces, dominated splitting., nonuniformly hyperbolic systems.

Mathematics Subject Classification: Primary: 37C05, 37E30, 37D25, 37D3.

Citation: Enrique R. Pujals, Federico Rodriguez Hertz. Critical points for surface diffeomorphisms. Journal of Modern Dynamics, 2007, 1 (4) : 615-648. doi: 10.3934/jmd.2007.1.615

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