Quasi-Periodic Motions in Families of Dynamical Systems : Order amidst Chaos. 1st ed. 1996

種類:

電子ブック

責任表示:

by Hendrik W. Broer, George B. Huitema, Mikhail B. Sevryuk

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1996

著者名:

• Broer, Hendrik W.
• Huitema, George B.
• Sevryuk, Mikhail B.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1645

ISBN:

9783540496137 [3540496130]    

注記:

and examples -- The conjugacy theory -- The continuation theory -- Complicated Whitney-smooth families -- Conclusions -- Appendices.
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

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