La conjecture de Herman

TL;DR

This paper proves a generalized KAM theorem confirming Michel Herman's conjecture about the existence of a positive measure set of invariant tori near elliptic Diophantine critical points in Hamiltonian systems.

Contribution

It introduces a formalism for UV-cutoff and establishes a generalized KAM theorem that resolves Herman's conjecture.

Findings

Existence of a positive measure set of invariant tori near elliptic Diophantine points

Development of a formalism for UV-cutoff in Hamiltonian systems

Proof of the generalized KAM theorem confirming Herman's conjecture

Abstract

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.