Flow map parameterization methods for invariant tori in Hamiltonian systems
Haro, Àlex (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
Mondelo González, José María (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2021
Abstract:	The goal of this paper is to present a methodology for the computation of invariant tori in Hamiltonian systems combining flow map methods, parameterization methods, and symplectic geometry. While flow map methods reduce the dimension of the tori to be computed by one (avoiding Poincaré maps), parameterization methods reduce the cost of a single step of the derived Newton-like method to be proportional to the cost of a FFT. Symplectic properties lead to some magic cancellations that make the methods work. The multiple shooting version of the methods are applied to the computation of invariant tori and their invariant bundles around librational equilibrium points of the Restricted Three Body Problem. The invariant bundles are the first order approximations of the corresponding invariant manifolds, commonly known as the whiskers, which are very important in the dynamical organization and have important applications in space mission design.
Grants:	Agencia Estatal de Investigación PGC2018-100699-B-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1374 European Commission 734557 Ministerio de Economía y Competitividad MDM-2014-0445 Ministerio de Economía y Competitividad MTM2014-52209-C2-1-P Agencia Estatal de Investigación MTM2016-80117-P Agencia Estatal de Investigación MTM2017-86795-C3-1-P
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Invariant tori ; Parameterization method ; KAM theory ; RTBP ; Lissajous orbits
Published in:	Communications in nonlinear science and numerical simulation, Vol. 101 (October 2021) , art. 105859, ISSN 1007-5704

DOI: 10.1016/j.cnsns.2021.105859

Postprint 53 p, 9.6 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles