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Chaos near resonance

Author: G Haller
Publisher: New York : Springer, ©1999.
Series: Applied mathematical sciences (Springer-Verlag New York Inc.), v. 138.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"This book offers the first systematic exposition of recent analytic results that can be used to understand and predict the global effect of resonances in phase space. The geometric methods discussed here enable one to identify complicated multi-time-scale solution sets and slow-fast chaos in physical problems. The topics include slow and partially slow manifolds, homoclinic and heteroclinic jumping, universal  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: G Haller
ISBN: 0387986979 9780387986975
OCLC Number: 40559731
Description: xvi, 427 pages : illustrations ; 24 cm.
Contents: 1. Concepts From Dynamical Systems --
2. Chaotic Jumping Near Resonances: Finite-Dimensional Systems --
3. Chaos Due to Resonances in Physical Systems --
4. Resonances in Hamiltonian Systems --
5. Chaotic Jumping Near Resonances: Infinite-Dimensional Systems --
App. A. Elements of Differential Geometry --
App. B. Some Facts From Analysis.
Series Title: Applied mathematical sciences (Springer-Verlag New York Inc.), v. 138.
Responsibility: G. Haller.
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Abstract:

A unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping.  Read more...

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"An extensive bibliography and the many examples make this clearly-written book an excellent introduction to these techniques for identifying chaos in perturbations of systems with resonance."Applied Read more...

 
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   schema:reviewBody ""This book offers the first systematic exposition of recent analytic results that can be used to understand and predict the global effect of resonances in phase space. The geometric methods discussed here enable one to identify complicated multi-time-scale solution sets and slow-fast chaos in physical problems. The topics include slow and partially slow manifolds, homoclinic and heteroclinic jumping, universal global bifurcations, generalized Silnikov-orbits and -manifolds, disintegration of invariant manifolds near resonances, and high-codimension homoclinic jumping. The main emphasis is on near-integrable dissipative systems, but a separate chapter is devoted to resonance phenomena in Hamiltonian systems. A number of applications are described from the areas of fluid mechanics, rigid body dynamics, chemistry, atmospheric science, and nonlinear optics. In addition, the theory is extended to infinite dimensions to cover resonances in certain nonlinear partial differential equations, such as single and coupled nonlinear Schrodinger equations."--BOOK JACKET. "This self-contained monograph will be useful to the applied scientist who wishes to analyze resonances in complex physical problems, as well as to mathematicians interested in the geometric theory of multi- and infinite-dimensional dynamical systems."--BOOK JACKET." ;
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