Chaos Near Resonance

Chaos Near Resonance

by G. Haller
     
 

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,… See more details below

Overview

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.. "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.

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Editorial Reviews

From the Publisher
"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 Mechanics Reviews, Vol. 53/4, April 2000

"Haller makes a point of wanting to see dynamical systems theory fulfil "its long-standing promise to solve real-life problems". His book, through a wealth of detailed examples, delivers on this promise, and is certain ti become a standard text in this area. In particular, it is an excellent introduction to this research area, and contains a wealth of bibliographical and historical detail.
Matthew Nicol, Bulletin of the LMS, No. 162, Vol. 33/3, May 2001

Product Details

ISBN-13:
9781461271727
Publisher:
Springer New York
Publication date:
04/30/2013
Series:
Applied Mathematical Sciences Series, #138
Edition description:
Softcover reprint of the original 1st ed. 1999
Pages:
430
Product dimensions:
6.14(w) x 9.21(h) x 0.91(d)

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