Unstable pressure and u-equilibrium states for partially hyperbolic diffeomorphsims

2017/10/08 by Huyi Hu, Hu, Huyi, Weisheng Wu +3 · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Protein Structure and Dynamics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1710.02816

openalex publication_date 2017/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Unstable pressure and u-equilibrium states are introduced and investigated for a partially hyperbolic diffeomorphsim f. We define the u-pressure P^u(f, φ) of f at a continuous function φ via the dynamics of f on local unstable leaves. A variational principle for unstable pressure P^u(f, φ), which states that P^u(f, φ) is the supremum of the sum of the unstable entropy and the integral of φ taken over all invariant measures, is obtained. U-equilibrium states at which the supremum in the variational principle attains and their relation to Gibbs u-states are studied. Differentiability properties of unstable pressure, such as tangent functionals, Gateaux differentiability and Fréchet differentiability and their relations to u-equilibrium states, are also considered.

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