Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/220218
Title: Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem
Author: Llave, Ramon de la
Celletti, Alessandra
Gimeno i Alquézar, Joan
Calleja, Renato
Keywords: Mecànica celeste
Sistemes dinàmics diferenciables
Celestial mechanics
Differentiable dynamical systems
Issue Date: 7-Nov-2023
Publisher: Springer Verlag
Abstract: We consider a Celestial Mechanics model: the spin–orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper is to show that it is possible to maintain the accuracy and reliability of the computation of quasi-periodic attractors for parameter values extremely close to the breakdown and, therefore, it is possible to obtain information on the breakdown mechanism of these quasi-periodic attractors. The method uses at the same time numerical and rigorous improvements to provide (i) a very accurate computation of the time-1 map of the spin–orbit problem (which reduces the dimensionality of the problem); (ii) a very efficient KAM method for maps which computes the attractor and its tangent spaces (by quadratically convergent, low storage requirements, and low operation count); (iii) explicit algorithms backed by a rigorous a posteriori KAM theorem, which establishes that if the algorithm is successful and produces a small residual, then there is a true solution nearby; and (iv) guaranteed algorithms to reach arbitrarily close to the border of existence as long as there are enough computer resources. As a by-product of the accuracy that we maintain till breakdown, we study several scale-invariant observables of the tori used in the renormalization group of infinite-dimensional spaces.
Note: Reproducció del document publicat a: https://doi.org/10.1007/s00332-023-09988-w
It is part of: Journal of Nonlinear Science, 2023, vol. 34
URI: https://hdl.handle.net/2445/220218
Related resource: https://doi.org/10.1007/s00332-023-09988-w
ISSN: 0938-8974
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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