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Regular and Chaotic Dynamics, 2025, Volume 30, Issue 4, Pages 538–549
DOI: https://doi.org/10.1134/S1560354725040057 (Mi rcd1319) 		 
Special Issue: Celebrating the 75th Birthday of V.V. Kozlov (Issue Editors: Sergey Bolotin, Vladimir Dragović, and Dmitry Treschev)

Singular KAM Theory for Convex Hamiltonian Systems

Santiago Barbieria, Luca Biascob, Luigi Chierchiab, Davide Zaccariac

a Departament d’Informàtica, Matemàtica Aplicada i Estadística, Universitat de Girona, 6 Campus Montilivi, 17003 Girona, Spain
b Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italy
c Department of Mathematics, University of Toronto, 40 St George St., M5S 2E4 Toronto, Canada
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DOI: https://doi.org/10.1134/S1560354725040057
Abstract: In this note, we briefly discuss how the singular KAM theory of [7] — which was worked out for the mechanical case $\frac12 |y|^2+\varepsilon f(x)$ — can be extended to convex real-analytic nearly integrable Hamiltonian systems with Hamiltonian in action-angle variables given by $h(y)+\varepsilon f(x)$ with $h$ convex and $f$ generic.
Keywords: nearly integrable Hamiltonian systems, convex Hamiltonians, measure of invariant tori, simple resonances, Arnold – Kozlov – Neishtadt conjecture, singular KAM theory
Funding agency
L. Biasco and L. Chierchia were supported by grant NRR-M4C2-I1.1-PRIN 2022-PE1-Stability in Hamiltonian dynamics and beyond-F53D23002730006-Financed by E.U.–NextGenerationEU. Santiago Barbieri was supported by the Juan de la Cierva Postdoctoral Grant JDC2023-052632-I funded by the Spanish National Agency for Research (Agencia Estatal de Investigación).
Received: 18.06.2025
Accepted: 18.07.2025
Document Type: Article
MSC: 37J05, 37J35, 37J40, 70H05, 70H08, 70H15
Language: English
Citation: Santiago Barbieri, Luca Biasco, Luigi Chierchia, Davide Zaccaria, “Singular KAM Theory for Convex Hamiltonian Systems”, Regul. Chaotic Dyn., 30:4 (2025), 538–549
Citation in format AMSBIB
\Bibitem{BarBiaChi25}
\by Santiago Barbieri, Luca Biasco, Luigi Chierchia, Davide Zaccaria
\paper Singular KAM Theory for Convex Hamiltonian Systems
\jour Regul. Chaotic Dyn.
\yr 2025
\vol 30
\issue 4
\pages 538--549
\mathnet{http://mi.mathnet.ru/rcd1319}
\crossref{https://doi.org/10.1134/S1560354725040057}
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