A dynamical condition for differentiability of Mather's average action

2012/08/07 by Alexandre B. Rocha, Rocha, Alexandre, Mário Carneiro +1
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1208.1474

openalex publication_date 2012/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the differentiability of β of Mather function on all homology classes corresponding to rotation vectors of measures whose supports are contained in a Lipschitz Lagrangian absorbing graph, invariant by Tonelli Hamiltonians. We also show the relationship between local differentiability of β and local integrability of the Hamiltonian flow.

Related

• Differentiability of Mather's average action and integrability on closed\n surfaces
• Differentiability of Mather's beta function in low dimensions
• Differentiability of Mather's β-function vs Mañé's conjecture
• Mather problem and viscosity solutions in the stationary setting
• Spectral invariants towards a Non-convex Aubry-Mather theory