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![The box V~(x~)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{V}(\tilde{x})$$\end{document} contained in the connected component of x~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{x}$$\end{document} on π-1(B(x,β))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi ^{-1}(B(x, \beta ))$$\end{document}, represented here for the two-dimensional case](publication/375914063/figure/fig2/AS:11431281214853875@1703818848821/The-box-Vxdocumentclass12ptminimal-usepackageamsmath-usepackagewasysym.png)
The box V~(x~)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{V}(\tilde{x})$$\end{document} contained in the connected component of x~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{x}$$\end{document} on π-1(B(x,β))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi ^{-1}(B(x, \beta ))$$\end{document}, represented here for the two-dimensional case
Source publication
![π-1(B(x,β))≃B(x,β)×π-1({x})\documentclass[12pt]{minimal}...](publication/375914063/figure/fig1/AS:11431281214853874@1703818848656/p-1Bx-bBx-bp-1xdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![The box V~(x~)\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/375914063/figure/fig2/AS:11431281214853875@1703818848821/The-box-Vxdocumentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
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...
