Mathieu Helfter (ISTA)
Abstract: The β-function describes the minimal average action associated with invariant measures of prescribed rotation number. We will discuss rigidity and possible flexibility properties of generalized standard maps defined by analytic potentials exhibiting KAM phenomena on a fixed set of Diophantine rotation numbers. In particular, we show that, generically, two such potentials have distinct infinite jets of their β-function at a given Diophantine rotation number or that non-degenerate deformations do not preserve the β-function.