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arXiv · 2003.01402

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

Carlo Carminati·Stefano Marmi·David Sauzin·Alfonso Sorrentino
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Abstract

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.

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Carlo Carminati, Stefano Marmi, David Sauzin, Alfonso Sorrentino. 2020-03-03. On the regularity of Mather's $\beta$-function for standard-like twist maps. https://arxiv.org/abs/2003.01402

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