Comptes Rendus
no. 4
Dynamical Systems
Backward volume contraction for endomorphisms with eventual volume expansion

Presented by: Jean-Christophe Yoccoz

José F. Alves1; Armando Castro2; Vilton Pinheiro2
1 Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
2 Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil
Comptes Rendus. Mathématique, Volume 342 (2006) no. 4, pp. 259-262.

We consider smooth maps on compact Riemannian manifolds. We prove that under some mild condition of eventual volume expansion Lebesgue almost everywhere we have uniform backward volume contraction on every pre-orbit of Lebesgue almost every point.

Nous considérons des transformations différentiables sur des varietés Riemannienes compactes. Nous montrons que dans une certaine condition modérée d'expansion de volume nous pouvons déduire que pour Lebesgue presque chaque point nous avons contraction uniforme de volume en arrière de chaque pré-orbite.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.11.024

José F. Alves 1; Armando Castro 2; Vilton Pinheiro 2

1 Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
2 Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil 
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José F. Alves; Armando Castro; Vilton Pinheiro. Backward volume contraction for endomorphisms with eventual volume expansion. Comptes Rendus. Mathématique, Volume 342 (2006) no. 4, pp. 259-262. doi : 10.1016/j.crma.2005.11.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.11.024/

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Cited by Sources:

⁎ Work carried out at the Federal University of Bahia. Partially supported by FCT through CMUP and UFBA.

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