Work

Nekhoroshev Theorem for time quasiperiodic perturbations of P-Steep systems

Year: 2026

Type: preprint

Abstract: We prove a Nekhoroshev type result for a time quasiperiodic perturbation of an integrable Hamiltonian system. More precisely, we assume that the integrable part is analytic and fulfills a generic nondegeneracy condition introduced by Nekhoroshev and called P-Steepness. We add a small perturbation which depends in a quasiperiodic way on time (with Diophantine frequency) and prove that -- for times exponentially long with the inverse of the size $\varepsilon$ of the perturbation -- the actions of the unperturbed system remain approximately constant. The proof is based on an extension to the time dependent case of the proof {of classical Nekhoroshev's theorem} given by Guzzo, Chierchia and Benettin, which however requires new ideas in order to deal with the more complex geometry of resonances of the time dependent case.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2606.30841

Authors: Bambusi, Dario, Barbieri, Santiago, Giralt, Mar, Langella, Beatrice

Institutions: University of Milan, Universitat de Girona, Université Paris Sciences et Lettres, Sorbonne Université, University of Pisa, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministero dell’Istruzione, dell’Università e della Ricerca, Institució Catalana de Recerca i Estudis Avançats, Sorbonne Université, Gruppo Nazionale per la Fisica Matematica

Award: G8974464479

OpenAlex ID: W7166802191

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