| 書目名稱 | Quasi-Periodic Motions in Families of Dynamical Systems | | 副標題 | Order amidst Chaos | | 編輯 | Hendrik W. Broer,George B. Huitema,Mikhail B. Sevr | | 視頻video | http://file.papertrans.cn/782/781614/781614.mp4 | | 叢書名稱 | Lecture Notes in Mathematics | | 圖書封面 |  | | 描述 | This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. Such a motion in the phase space densely fills up an invariant torus. This phenomenon is most familiar from Hamiltonian dynamics. Hamiltonian systems are well known for their use in modelling the dynamics related to frictionless mechanics, including the planetary and lunar motions. In this context the general picture appears to be as follows. On the one hand, Hamiltonian systems occur that are in complete order: these are the integrable systems where all motion is confined to invariant tori. On the other hand, systems exist that are entirely chaotic on each energy level. In between we know systems that, being sufficiently small perturbations of integrable ones, exhibit coexistence of order (invariant tori carrying quasi-periodic dynamics) and chaos (the so called stochastic layers). The Kolmogorov-Arnol‘d-Moser (KAM) theory on quasi-periodic motions tells us that the occurrence of such motions is open within the class of all Hamiltonian systems: in other words, it is a phenomenon persistent under small Hamiltonian perturbations. Moreover, generally, for any such system the union of quasi-periodic | | 出版日期 | Book 1996 | | 關鍵詞 | Chaos; KAM-theory; analysis; dynamical systems; hamiltonian systems; reversible systems; stability; systems | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-540-49613-7 | | isbn_softcover | 978-3-540-62025-9 | | isbn_ebook | 978-3-540-49613-7Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer-Verlag Berlin Heidelberg 1996 |
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