Robustness and uniqueness of equilibrium states for certain partially hyperbolic systems
Mongez, Juan Carlos, Pacifico, Maria José
Dynamical Systems · Ergodic Theory
Juan Carlos
Mongez
Juan Carlos Mongez is a postdoctoral researcher at the University of São Paulo, currently on a research stay at Université Paris-Saclay, hosted by Sylvain Crovisier. His research lies in smooth dynamical systems and ergodic theory, with an emphasis on measures of maximal entropy and partially hyperbolic dynamics.
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Research
I study the ergodic and topological properties of smooth dynamical systems beyond uniform hyperbolicity.
A central theme of my work is understanding existence, finiteness, uniqueness, and stability of measures of maximal entropy for partially hyperbolic diffeomorphisms. I am also interested in equilibrium states, entropy, symbolic codings, dominated splittings, and non-uniform hyperbolicity.
- Smooth dynamical systems
- Ergodic Theory
- Partially hyperbolic dynamics
- Measures of maximal entropy
- Thermodynamic formalism
- Symbolic dynamics
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Publications
Partially hyperbolic diffeomorphisms with a finite number of measures of maximal entropy
Mongez, Juan Carlos, Pacifico, Maria José, Poletti, Mauricio
Symbolic dynamics for non-uniformly hyperbolic flows in high dimension
Lima, Yuri, Mongez, Juan Carlos, Nascimento, João Paulo
Finite measures of maximal entropy for an open set of partially hyperbolic diffeomorphisms
Mongez, Juan Carlos, Pacifico, Maria Jose
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Academic Career
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Visiting Researcher
Université Paris-Saclay, France
Hosted by Sylvain Crovisier · During postdoctoral appointment at IME-USP
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Postdoctoral Researcher
Instituto de Matemática e Estatística — Universidade de São Paulo
Supervisor: Yuri Lima · FAPESP
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Postdoctoral Researcher
Universidade Federal do Ceará, Fortaleza
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Ph.D. in Mathematics
Universidade Federal do Rio de Janeiro
Advisors: Maria José Pacifico · Jiagang Yang
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M.Sc. in Mathematics
Universidade Federal do Rio de Janeiro
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B.Sc. in Mathematics
Universidad Centroccidental Lisandro Alvarado, Venezuela
Outreach
Mathematical Olympiads
During his undergraduate studies at the Universidad Centroccidental Lisandro Alvarado (UCLA) in Venezuela, Juan Carlos was actively involved in organising and coaching students for mathematical olympiads. He contributed to training sessions and problem-solving workshops aimed at preparing young Venezuelan students for national and regional mathematical competitions.
Contact
Let's talk mathematics.
For questions, collaborations, seminars, or research visits, feel free to get in touch.
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