Critical points for surface diffeomorphisms

Enrique R. Pujals; Federico Rodriguez Hertz

doi:10.3934/jmd.2007.1.615

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2007, Volume 1, Issue 4: 615-648. Doi: 10.3934/jmd.2007.1.615

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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
2.
IMERL-Facultad de Ingeniería, Universidad de la República, ulio Herrera y Reissig 565, CC 30, 11300 Montevideo

Received: January 31, 2007

Revised: July 31, 2007

Published: June 2007

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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.

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Mathematics Subject Classification: Primary: 37C05, 37E30, 37D25, 37D30.

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