Details

Autor(en) / Beteiligte

• Carminati, Carlo
• Marmi, Stefano
• Sauzin, David
• Sorrentino, Alfonso

Titel

On the regularity of Mather's $\beta$-function for standard-like twist maps

Ist Teil von

• Advances in mathematics (New York. 1965), 2020-03, Vol.377

Ort / Verlag

Elsevier

Erscheinungsjahr

2020

Link zum Volltext

Quelle

Free E-Journal (出版社公開部分のみ）

Beschreibungen/Notizen

• We consider the minimal average action (Mather's $\beta$ 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 $\beta$-function associated to a standard-like twist map admits a unique $C^1$-holomorphic complex extension, which coincides with this function on the set of real diophantine frequencies.