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Chaos Near Resonance

by G. Haller

  • ISBN: 9780387986975
  • ISBN10: 0387986979

Chaos Near Resonance

by G. Haller

  • List Price: $159.99
  • Binding: Hardcover
  • Publisher: Springer Verlag
  • Publish date: 09/01/1999
  • ISBN: 9780387986975
  • ISBN10: 0387986979
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Description: This book offers the first systematic exposition of recent analytic results that can be used to understand & predict the global effect of resonances in phase space. The geometric methods discussed here enable one to identify complicated multi-time-scale solution sets & slow-fast chaos in physical problems. The topics include slow & partially slow manifolds, homoclinic & heteroclinic jumping, universal global bifurcations, generalized (vS)ilnikov orbits & manifolds, disintegration of invariant manifolds near resonances & 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 & nonlinear optics. In addition, the theory is extended to infinite dimensions to cover resonances in certain nonlinear partial differential equations, such as single & coupled nonlinear Schr(ddot o)dinger equations. This self-contained monograph should be useful to mathematicians interested in the geometric theory of multi-and infinite-dimensional dynamical systems, as well as to the applied scientist who wishes to analyze resonances in physical problems.
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