Physics-Mechanics: Nonlinear dynamics and chaos

Chaos Near Resonance

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Title (user) : Chaos Near ResonanceISBN : 0387986979,9780387986975DDC : 003.857LCC : Q172.5.C45H345 1999DOI : 10.1007/978-1-4612-1508-0GoogleBook ID : w0Q2FGki6TkCOpenLibrary ID : OL18136481MEdition : 1Series : Applied Mathematical Sciences 138Autho...
Description

Title (user) : Chaos Near Resonance

ISBN : 0387986979,9780387986975

DDC : 003.857

LCC : Q172.5.C45H345 1999

DOI : 10.1007/978-1-4612-1508-0

GoogleBook ID : w0Q2FGki6TkC

OpenLibrary ID : OL18136481M

Edition : 1

Series : Applied Mathematical Sciences 138

Authors (user) : G. Haller (auth.)

Authors (google) : G. Haller

Publisher : Springer-Verlag New York

Language : English

Publication Date : 1999

Scanned : yes (300 DPI)

File Format : djvu

Categories : Mathematics


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Description (user) :

Resonances are ubiquitous in dynamical systems with many degrees of freedom. They have the basic effect of introducing slow-fast behavior in an evolutionary system which, coupled with instabilities, can result in highly irregular behavior. This book gives a unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, a general finite dimensional theory of homoclinic jumping is developed and illustrated with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context. Previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds are described. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics. The theory is further used to study resonances in Hamiltonian systems with applications to molecular dynamics and rigid body motion. The final chapter contains an infinite dimensional extension of the finite dimensional theory, with application to the perturbed nonlinear Schrödinger equation and coupled NLS equations.


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Description (google) :
A unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, the book develops a general finite dimensional theory of homoclinic jumping, illustrating it with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics.


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Table of contents :
Front Matter....Pages i-xvi
Concepts From Dynamical Systems....Pages 1-55
Chaotic Jumping Near Resonances: Finite-Dimensional Systems....Pages 56-158
Chaos Due to Resonances in Physical Systems....Pages 159-230
Resonances in Hamiltonian Systems....Pages 231-285
Chaotic Jumping Near Resonances: Infinite-Dimensional Systems....Pages 286-370
Back Matter....Pages 371-430

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