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Differentiability of thermodynamic quantities for partially hyperbolic systems

Grant number: 17/08732-1
Support Opportunities:Regular Research Grants
Start date: August 01, 2017
End date: July 31, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Suzete Maria Silva Afonso
Grantee:Suzete Maria Silva Afonso
Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
Associated researchers: Jaqueline Siqueira Rocha ; Vanessa Ribeiro Ramos

Abstract

In this project we propose the study of the thermodynamical formalism for a class of partially hyperbolic systems associated to regular potentials. We start with the study of a family of partially hyperbolic horseshoes for which we obtain linear response formulas for the equilibrium states associated to Hölder continuous potentials with small variation. Then we study partially hyperbolic skew-products whose base is a non-uniformly expanding map. For these systems we enlarge the class of potential for which we guarantee existence and finiteness of equilibrium states. Next we show that certain thermodynamical quantities such as topological entropy, topological pressure and correlation function (for the maximal entropy measure) are differentiable. Finally we consider step skew products, or skew products given by a iterated functions system and we exhibit sufficient conditions (on the iterated functions system and on the potentials) for the existence and finiteness of equilibrium states. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
AFONSO, SUZETE MARIA; RAMOS, VANESSA; SIQUEIRA, JAQUELINE. EQUILIBRIUM STATES FOR NON-UNIFORMLY HYPERBOLIC SYSTEMS: STATISTICAL PROPERTIES AND ANALYTICITY. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 41, n. 9, p. 29-pg., . (17/08732-1)