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 (canonical) complex extension, which coincides with this function on the set of real diophantine frequencies. In particular, we deduce a uniqueness result for Mather’s β function.
Carminati, C., Marmi, S., Sauzin, D., Sorrentino, A. (2020). On the regularity of Mather's β-function for standard-like twist maps. ADVANCES IN MATHEMATICS, 107460 [10.1016/j.aim.2020.107460].
On the regularity of Mather's β-function for standard-like twist maps
Sorrentino A.
2020-11-01
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 (canonical) complex extension, which coincides with this function on the set of real diophantine frequencies. In particular, we deduce a uniqueness result for Mather’s β function.| File | Dimensione | Formato | |
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