Robustness and uniqueness of equilibrium states for certain partially hyperbolic systems

2023/06/21 by Juan Carlos Mongez, Mongez, Juan Carlos, Maria José Pacífico +1 · 3 citations
Engineering · Mathematics · #37D35 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2306.12323

openalex publication_date 2023/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

We prove that if f is a C¹⁺ partially hyperbolic diffeomorphism satisfying certain conditions then there is a C¹-open neighborhood \cA of f so that every g∈ \cA∩ Diff¹⁺(M) has a unique equilibrium state.

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• On equilibrium states for certain partially hyperbolic endomorphisms with one-dimensional center
• Unique equilibrium states for some partially hyperbolic diffeomorphisms with dominated splittings
• Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms

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