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| Author(s): |
Jorge Luis Crisostomo Parejas
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2016-09-26 |
| Examining board members: |
Carlos Alberto Maquera Apaza;
Renaud Daniel Jacques Leplaideur;
Samuel Anton Senti;
José Régis Azevedo Varão Filho
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| Advisor: | Ali Tahzibi |
| Abstract | |
We address the problem of existence and uniqueness (or finiteness) of ergodic equilibrium states for a natural class of partially hyperbolic diffeomorphisms homotopic to Anosov. We propose to study the disintegration of equilibrium states along the central foliation as a tool to develop the theory of equilibrium states for partially hyperbolic dynamics. For a large class of low variational potentials we obtain existence and uniqueness of the equilibrium state and we also obtain a dichotomy between finiteness of ergodic equilibrium states and hyperbolicity of such measures. We also prove that the measure of maximal entropy for accessible partially hyperbolic diffeomorphisms of 3-manifold having compact center leaves can be written locally as the product of three measures defined on the local stable, central and unstable foliations provided that such measure is unique. We verify that the local product structure does not hold when the number of measures of maximal entropy is larger than one. (AU) | |
| FAPESP's process: | 13/03735-1 - Foliations, transverse measures and partially hyperbolic systems |
| Grantee: | Jorge Luis Crisostomo Parejas |
| Support Opportunities: | Scholarships in Brazil - Doctorate |