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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

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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