JournalsaihpcVol. 30, No. 1pp. 101–120

Geometry of expanding absolutely continuous invariant measures and the liftability problem

  • José F. Alves

    Departamento de Matemática, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal

  • Carla L. Dias

    Instituto Politécnico de Portalegre, Lugar da Abadessa, Apartado 148, 7301-901 Portalegre, Portugal

  • Stefano Luzzatto

    Mathematics Department, Imperial College, 180 Queenʼs Gate, London SW7, UK
Geometry of expanding absolutely continuous invariant measures and the liftability problem cover
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Abstract

We show that for a large class of maps on manifolds of arbitrary finite dimension, the existence of a Gibbs–Markov–Young structure (with Lebesgue as the reference measure) is a necessary as well as sufficient condition for the existence of an invariant probability measure which is absolutely continuous measure (with respect to Lebesgue) and for which all Lyapunov exponents are positive.

Cite this article

José F. Alves, Carla L. Dias, Stefano Luzzatto, Geometry of expanding absolutely continuous invariant measures and the liftability problem. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 1, pp. 101–120

DOI 10.1016/J.ANIHPC.2012.06.004