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In the Nineties, Michel Herman conjectured the existence of a positive measure set of invariant tori at an elliptic diophatine critical point of a hamiltonian function. I construct a formalism for the UV-cutoff and prove a generalised KAM theorem which solves positively the Herman conjecture.
In the nineties, Michel Herman conjectured the existence of a positive measure set of invariant tori at an elliptic diophantine critical point of a hamiltonian function. I show that KAM versal deformation theory solves positively this conjecture.
In this note, we extend the renormalization horseshoe we have recently constructed with N. Goncharuk for analytic diffeomorphisms of the circle to their small two-dimensional perturbations. As one consequence, Herman rings with rotation numbers of bo
Les travaux presentes dans ce memoire portent sur la dynamique de diffeomorphismes de varietes compactes. Pour letude des proprietes generiques ou pour la construction dexemples, il est souvent utile de savoir perturber un syst`eme. Ceci soul`eve gen
This survey article is the written version of a talk given at the Bourbaki seminar in April 2021. We give an introduction to Zagiers conjecture on special values of Dedekind zeta functions, and its relation to $K$-theory of fields and the theory of m
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