Figure - available from: Journal of Statistical Physics
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π-1(B(x,β))≃B(x,β)×π-1({x})\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi ^{-1}(B(x, \beta )) \simeq B(x, \beta ) \times \pi ^{-1}(\{x\})$$\end{document} represented for a two-dimensional case, in which we have dynamical coherence and the center leaves are well defined
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We prove the existence of equilibrium states for partially hyperbolic endomorphisms with one-dimensional center bundle. We also prove, regarding a class of potentials, the uniqueness of such measures for endomorphisms defined on the 2-torus that: have a linear model as a factor; and with the condition that this measure gives zero weight to the set...