Reminiscences on science at I.H.E.S. A problem on homoclinic theory and a brief review

TL;DR

This paper reflects on the author's scientific experiences at IHES, culminating in the presentation of a convergent perturbative algorithm for constructing Eliasson's potential related to invariant tori's stable and unstable manifolds.

Contribution

It introduces a new convergent perturbative algorithm for Eliasson's potential, advancing the study of invariant tori in homoclinic theory.

Findings

Development of a convergent perturbative algorithm

Analysis of the properties of Eliasson's potential

Application to stable and unstable manifolds

Abstract

On the occasion of the 40-th anniversary of IHES I present a few scientific reminiscences: most of my scientific life has been marked by my visits and I run through them concluding with the analysis of a problem that originated during my last visit. The problem is to develop a convergent perturbative algorithm for the construction of the ``Eliasson's potential'' for the stable and unstable manifolds of an invariant torus: and to study its properties. A brief review follows.