Physical measures for partially hyperbolic surface endomorphisms

By M. Tsujii. 2003

69 citations recorded by the source corpus.

We consider dynamical systems generated by partially hyperbolic surface endomorphisms of class C^r with one-dimensional strongly unstable subbundle. As the main result, we prove that such a dynamical system generically admits finitely many ergodic physical measures whose union of basins of attraction has total Lebesgue measure, provided that r>= 19.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9aa746e9e03e2caea120cca5c3b7823dff857089

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

SRB measures for partially hyperbolic systems whose central direction is weakly expanding (2014, unknown): “…but the same kind of questions, and the Palis conjecture, also apply to endomorphisms—see for example [9, 10, 17, 24, 32, 31] for the setting of one-dimensional maps, [45] in two dimensions, and [5, 6, 40, 41] for the construction of SRB measures in certain higher-dimensional settings.”
Physical measures and absolute continuity for one-dimensional center direction (2013, background): “In a remarkable recent paper, Tsujii [59] proved that generic (dense Gδ) partially hyperbolic surface endomorphisms do admit finitely many physical measures, such that the union of their basins has full Lebesgue measure.”
Generic family with robustly infinitely many sinks (2014, background): “e result of Kozlovski, Shen and van Strien showing the density of hyperbolicity for multimodal maps [KSvS07]. Palis conjecture is well known to be true for dynamics which are uniformly hyperbolic. In [Tsu05], Tsuji showed that a generic partially hyperbolic Cr-maps of the 2-torus (with a strong unst”