Mathematical Physics

Download E-books Quasi-Periodic Motions in Families of Dynamical Systems: Order amidst Chaos (Lecture Notes in Mathematics) PDF

This publication is dedicated to the phenomenon of quasi-periodic movement in dynamical platforms. this kind of movement within the section house densely fills up an invariant torus. This phenomenon is so much usual from Hamiltonian dynamics. Hamiltonian structures are popular for his or her use in modelling the dynamics concerning frictionless mechanics, together with the planetary and lunar motions. during this context the final photograph seems to be as follows. at the one hand, Hamiltonian structures happen which are in whole order: those are the integrable platforms the place all movement is restrained to invariant tori. nevertheless, structures exist which are totally chaotic on each one strength point. In among we all know platforms that, being small enough perturbations of integrable ones, express coexistence of order (invariant tori wearing quasi-periodic dynamics) and chaos (the so known as stochastic layers). The Kolmogorov-Arnol'd-Moser (KAM) thought on quasi-periodic motions tells us that the prevalence of such motions is open in the type of all Hamiltonian platforms: in different phrases, it's a phenomenon chronic lower than small Hamiltonian perturbations. furthermore, usually, for one of these process the union of quasi-periodic tori within the part house is a nowhere dense set of confident Lebesgue degree, a so known as Cantor family members. This truth signifies that open sessions of Hamiltonian structures exist that aren't ergodic. the most objective of the publication is to check the alterations during this photo while different periods of platforms - or contexts - are thought of.

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