Flow map parameterization methods for invariant tori in Hamiltonian systems
| Autor: | Àlex Haro, Josep-Maria Mondelo |
|---|---|
| Přispěvatelé: | Ministerio de Ciencia, Innovación y Universidades (España), Ministerio de Economía y Competitividad (España) |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Computation Lissajous orbits KAM theory Dynamical Systems (math.DS) Space (mathematics) 01 natural sciences 010305 fluids & plasmas Hamiltonian system Dimension (vector space) 0103 physical sciences FOS: Mathematics Flow map Invariant (mathematics) Mathematics - Dynamical Systems 010306 general physics Mathematics::Symplectic Geometry Mathematics Numerical Analysis RTBP Invariant tori Kolmogorov–Arnold–Moser theorem Applied Mathematics Modeling and Simulation Parameterization method Symplectic geometry |
| Zdroj: | Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona Digital.CSIC. Repositorio Institucional del CSIC instname |
| DOI: | 10.48550/arxiv.2101.07665 |
| Popis: | 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. A.H. is supported by the grants PGC2018-100699-B-I00 (MCIU-AEI-FEDER, UE), 2017 SGR 1374 (AGAUR), MSCA 734557 (EU Horizon 2020), and MDM-2014-0445 (MINECO), and by the NSF under Grant No. 1440140 to found his residence at MSRI in Berkeley, California, during the Fall 2018 semester. J.M. Mondelo has been supported by the MINECO-AEI grant MTM2014-52209-C2-1-P and the MICINN-AEI grants MTM2016-80117-P, MTM2017-86795-C3-1-P, PID2019-104851GB-I00. |
| Databáze: | OpenAIRE |
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