On the regularity of Mather's β-function for standard-like twist maps
| Autor: | Alfonso Sorrentino, David Sauzin, Carlo Carminati, Stefano Marmi |
|---|---|
| Přispěvatelé: | Carminati, C., Marmi, S., Sauzin, D., Sorrentino, A. |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems General Mathematics Diophantine equation Mather's beta function 010102 general mathematics Holomorphic function Annulus (mathematics) Function (mathematics) Extension (predicate logic) 01 natural sciences Twist maps Action (physics) Standard map Aubry-Mather theory 0103 physical sciences Settore MAT/05 010307 mathematical physics Uniqueness 0101 mathematics Twist Settore MAT/07 - Fisica Matematica Mathematics |
| Popis: | 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 C 1 -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. |
| Databáze: | OpenAIRE |
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