The Herman conjecture

TL;DR

This paper confirms Michel Herman's conjecture by applying KAM versal deformation theory, demonstrating the existence of a positive measure set of invariant tori at specific elliptic points in Hamiltonian systems.

Contribution

It provides a proof that KAM versal deformation theory affirms Herman's conjecture regarding invariant tori in Hamiltonian dynamics.

Findings

Positive measure set of invariant tori exists at elliptic Diophantine critical points.

KAM versal deformation theory effectively solves the conjecture.

Supports the stability and structure of Hamiltonian systems.

Abstract

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.