| Description |
1 online resource (xv, 237 pages) : illustrations |
| Series |
Lecture notes in mathematics, 0075-8434 ; 1893 |
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Lecture notes in mathematics (Springer-Verlag) ; 1893.
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| Contents |
Introduction -- Bifurcations of equilibria -- Bifurcations of periodic orbits -- Bifurcations of invariant tori -- Perturbations of ramified torus bundles -- Planar singularities -- Stratifications -- Normal form theory -- Proof of the main KAM theorem -- Proofs of the necessary lemmata |
| Summary |
Once again KAM theory is committed in the context of nearly integrable Hamiltonian systems. While elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Hence, without the need for untypical conditions or external parameters, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system. The text moves gradually from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations have to be replaced by Cantor sets. Planar singularities and their versal unfoldings are an important ingredient that helps to explain the underlying dynamics in a transparent way |
| Bibliography |
Includes bibliographical references (pages 219-233) and index |
| Notes |
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
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English |
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Print version record |
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digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL |
| Subject |
Hamiltonian systems.
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Bifurcation theory.
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MATHEMATICS -- Differential Equations -- General.
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Bifurcation theory.
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Hamiltonian systems.
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Bifurcation theory
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Hamiltonian systems
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Hamiltonsches System
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Verzweigung Mathematik
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Dynamisches System
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Dynamische systemen.
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Bifurcatie.
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Hamiltonianen.
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Hamiltonian systems.
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Bifurcation theory.
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Verzweigung <Mathematik>
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| Form |
Electronic book
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| ISBN |
9783540388968 |
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3540388966 |
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354038894X |
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9783540388944 |
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9786611069759 |
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6611069755 |
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