Robustness and uniqueness of equilibrium states for certain partially hyperbolic systems<sup>*</sup>
Abstract We prove that if f is a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> partially hyperbolic diffeomorphism satisfying certain conditions then there is a C 1 -open neighborhood <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">A</mml:mi> </mml:mrow> </mml:mrow> </mml:math> of f so that every <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>∈</mml:mo> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">A</mml:mi> </mml:mrow> <mml:mo>∩</mml:mo> <mml:msup> <mml:mi>Diff</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> <mml:mo></mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>M</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> has a unique equilibrium state.
Authors
- Maria José Pacífico (ORCID: https://orcid.org/0000-0002-7677-5668)
- Juan Carlos Mongez
Institutions
- Universidade Federal do Rio de Janeiro (BR)
Publication Details
- Journal
- Nonlinearity
- Published
- 2025-02-21
- DOI
- https://doi.org/10.1088/1361-6544/adb52f
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro