Mathieu Helfter

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20222026

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math.DS2026

Jet rigidity of Mather's $β$ -function and complexified KAM curves holomorphic in potential for analytic standard maps

Mathieu Helfter

Mather's $β$ -function associates with each rotation number the least average action carried by an orbit of a twist map. For analytic standard maps in the KAM regime, we prove the f…

math.DS2022

Every diffeomorphism is a total renormalization of a close to identity map

Pierre Berger, Nicolaz Gourmelon, Mathieu Helfter

For any $1 \leq r \leq \infty$ , we show that every diffeomorphism of a manifold of the form $R / Z \times M$ is a total renormalization of a $C^{r}$ -close to identity map…

math.DS2022

Scales

Mathieu Helfter

We introduce the notion of scale to generalize and compare different invariants of metric spaces and their measures. Several versions of scales are introduced such as Hausdorff, pa…

Jet rigidity of Mather's β-function and complexified KAM curves holomorphic in potential for analytic standard maps

Every diffeomorphism is a total renormalization of a close to identity map

Scales

Jet rigidity of Mather's $β$ -function and complexified KAM curves holomorphic in potential for analytic standard maps