On the convergence of flow map parameterization methods for whiskered tori in quasi-periodic Hamiltonian systems
Fernandez-Mora, Álvaro (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
Haro, Àlex (Centre de Recerca Matemàtica)
Mondelo, Josep Maria (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2026
Abstract:	We obtain an a-posteriori theorem for the existence of partially hyperbolic invariant tori in analytic Hamiltonian systems: autonomous, periodic, and quasi-periodic. The method of proof is based on the convergence of a KAM iterative scheme to solve the invariance equations of tori and their invariant bundles under the framework of the parameterization method. Starting from parameterizations analytic in a complex strip and satisfying their invariance equations approximately, we derive conditions for the existence of analytic parameterizations in a smaller strip satisfying the invariance equations exactly. The proof relies on the careful treatment of the analyticity loss with each iterative step and on the control of geometric properties of symplectic flavour. We also provide all the necessary explicit constants to perform computer-assisted proofs.
Grants:	Agencia Estatal de Investigación PID2021-125535NB-I00 Agencia Estatal de Investigación PID2020-118281GB-C31 Generalitat de Catalunya 2021/SGR-00113 Agencia Estatal de Investigación CEX2020-001084-M
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	KAM theory ; Parameterization method ; Invariant tori ; Quasi-periodic Hamiltonian systems
Published in:	Communications in nonlinear science and numerical simulation, Vol. 152, Num. Part B (January 2026) , art. 109214, ISSN 1878-7274

DOI: 10.1016/j.cnsns.2025.109214

39 p, 4.0 MB

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