Abstract:
We consider nearly-integrable systems under a relatively small dissipation. In particular we investigate two specific models: the discrete dissipative standard map and the continuous dissipative spin-orbit model. With reference to such samples, we review some analytical and numerical results about the persistence of invariant attractors and of periodic attractors.
\Bibitem{Cel09}
\by A. Celletti
\paper Periodic and Quasi-periodic Attractors of Weakly-dissipative Nearly-integrable Systems
\jour Regul. Chaotic Dyn.
\yr 2009
\vol 14
\issue 1
\pages 49--63
\mathnet{http://mi.mathnet.ru/rcd540}
\crossref{https://doi.org/10.1134/S1560354709010067}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2480952}
\zmath{https://zbmath.org/?q=an:1229.70074}
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This publication is cited in the following 8 articles:
Xiaodan Xu, Wen Si, Jianguo Si, “The p : q resonance for dissipative spin–orbit problem in celestial mechanics”, Z. Angew. Math. Phys., 75:6 (2024)
Sawsan Alhowaity, Elbaz I. Abouelmagd, Zouhair Diab, Juan L. G. Guirao, “Calculating periodic orbits of the Hénon–Heiles system”, Front. Astron. Space Sci., 9 (2023)
Stefano Pierini, Mickaël D. Chekroun, Michael Ghil, “The onset of chaos in nonautonomous dissipative dynamical systems: a low-order ocean-model case study”, Nonlin. Processes Geophys., 25:3 (2018), 671
Houyu Zhao, Liu Tian, “Analytic invariant curves for an iterative equation related to dissipative standard map”, Math Methods in App Sciences, 40:10 (2017), 3733
Letizia Stefanelli, Ugo Locatelli, “Quasi-periodic motions in a special class of dynamical equations with dissipative effects: A pair of detection methods”, DCDS-B, 20:4 (2015), 1155
CORRADO FALCOLINI, LAURA TEDESCHINI-LALLI, “HÉNON MAP: SIMPLE SINKS GAINING COEXISTENCE AS b → 1”, Int. J. Bifurcation Chaos, 23:09 (2013), 1330030
Renato C. Calleja, Alessandra Celletti, Rafael de la Llave, “A KAM theory for conformally symplectic systems: Efficient algorithms and their validation”, Journal of Differential Equations, 255:5 (2013), 978
Letizia Stefanelli, Ugo Locatelli, “Kolmogorov's normal form for equations of motion with dissipative effects”, Discrete & Continuous Dynamical Systems - B, 17:7 (2012), 2561
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