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arXiv · 2601.18268

Improved stability estimates at elliptic equilibria of Hamiltonian systems

Massimiliano Guzzo·Chiara Caracciolo·Gabriella Pinzari
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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.

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BibTeXRIS

Massimiliano Guzzo, Chiara Caracciolo, Gabriella Pinzari. 2026-01-26. Improved stability estimates at elliptic equilibria of Hamiltonian systems. https://arxiv.org/abs/2601.18268

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