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Chaos Near Resonance

Overview

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of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse ...

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Paperback (Softcover reprint of the original 1st ed. 1999)
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Overview

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of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds.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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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

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Product Details

  • ISBN-13: 9781461271727
  • Publisher: Springer New York
  • Publication date: 4/30/2013
  • Series: Applied Mathematical Sciences Series , #138
  • Edition description: Softcover reprint of the original 1st ed. 1999
  • Edition number: 1
  • Pages: 430
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.91 (d)

Table of Contents

Preface
1 Concepts From Dynamical Systems 1
2 Chaotic Jumping Near Resonances: Finite-Dimensional Systems 56
3 Chaos Due to Resonances in Physical Systems 159
4 Resonances in Hamiltonian Systems 231
5 Chaotic Jumping Near Resonances: Infinite-Dimensional Systems 286
App. A Elements of Differential Geometry 371
App. B Some Facts From Analysis 390
References 401
Symbol Index 421
Index 423
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