Improved stability estimates at elliptic equilibria of Hamiltonian systems
Abstract
This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian system satisfying a non-resonance condition of finite order N. In particular, we improve the standard a-priori lower bound on the stability time from a purely linear dependence on the inverse of the polynomial norm of the remainder of the normal form to the sum of a linear term (which is still present but with a different constant coefficient) and a quadratic one. The prevalence between the linear and the quadratic term depends on the resonance properties of all the monomials in the remainder of the normal form with degree from N to a finite order M. We also provide a comparative example of the new estimates and the traditional a priori ones in the framework of computer-assisted proofs.
Keywords
Cite
@article{arxiv.2601.18268,
title = {Improved stability estimates at elliptic equilibria of Hamiltonian systems},
author = {Massimiliano Guzzo and Chiara Caracciolo and Gabriella Pinzari},
journal= {arXiv preprint arXiv:2601.18268},
year = {2026}
}