On the regularity of Mather's β-function for standard-like twist maps

2020/03/03 by Carlo Carminati, Carminati, Carlo, Stefano Marmi +5
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2003.01402

openalex publication_date 2020/03/03 · openalex created_date 2020/03/13 · openalex updated_date 2026/07/28

Abstract

We consider the minimal average action (Mather's β function) for area preserving twist maps of the annulus. The regularity properties of this function share interesting relations with the dynamics of the system. We prove that the β-function associated to a standard-like twist map admits a unique C¹-holomorphic complex extension, which coincides with this function on the set of real diophantine frequencies.

Citations

• A universal instability of many-dimensional oscillator systems

Related

• There is only one KAM curve
• Regularity properties of critical invariant circles of twist maps, and their universality
• Moser's twist theorem revisited
• A note on a standard family of twist maps
• Hyperbolicity for conservative twist maps of the 2-dimensional annulus