La conjecture de Herman

2011/04/05 by Mauricio Garay, Garay, Mauricio
Social Sciences · #Dynamical Systems (math.DS) #FOS: Mathematics #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.1104.0748

openalex publication_date 2011/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• The Herman conjecture
• The Herman invariant tori conjecture
• Positive measure of KAM tori for finitely differentiable Hamiltonians
• Singular KAM Theory
• Converse KAM theory revisited