Physical measures under the hyperbolicity of pseudo-physical measures (Q6540597)

The main result of this paper establishes the existence of Sinai-Ruelle-Bowen measures (called ``physical measures'' by the authors) for a class of diffeomorphisms that allow a dominated splitting \(TM = E^{cu} \oplus E^{cs}\), such that any pseudo-physical measure allows only positive Lyapunov exponents along \(E^{cu}\) and negative Lyapunov exponents along \(E^{cs}\). Here \(M\) is a compact Riemannian manifold. The authors also prove that there is only a finite number of such measures. Further, the basins of the physical measures cover a full Lebesgue measure subset of \(M\).\N\NPseudo-measures (also known as SRB-like measures) were introduced in [\textit{E. Catsigeras} and \textit{H. Enrich}, Bull. Pol. Acad. Sci., Math. 59 No. 2, 151--164 (2011; Zbl 1248.37007)].