Open AccessKolmogorov's normal form for equations of motion with dissipative effects
Author(s) -
Letizia Stefanelli,
Ugo Locatelli
Publication year - 2012
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2012.17.2561
Subject(s) - dissipative system , integrable system , attractor , phase space , invariant (physics) , classical mechanics , torus , action (physics) , isotropy , equations of motion , physics , normalization (sociology) , motion (physics) , dynamical systems theory , mathematical analysis , mathematics , mathematical physics , geometry , quantum mechanics , sociology , anthropology
We focus on the equations of motion related to the "dissipative spin-orbit model", which is commonly studied in Celestial Mechanics. We consider them in the more general framework of a 2n-dimensionalaction-angle phase space. Since the friction terms are assumed to be linear and isotropic with respect to the action variables, the Kolmogorov's normalization algorithm for quasi-integrable Hamiltonians can be easily adapted to the dissipative system considered here. This allows us to prove the existence of quasi-periodic invariant tori that are local attractors