Hanßmann, H: Local and Semi-Local Bifurcations
Results and Examples. Book w. online files/update
(Sprache: Englisch)
This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian...
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Produktinformationen zu „Hanßmann, H: Local and Semi-Local Bifurcations “
This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.
Klappentext zu „Hanßmann, H: Local and Semi-Local Bifurcations “
This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.
Inhaltsverzeichnis zu „Hanßmann, H: Local and Semi-Local Bifurcations “
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.
Bibliographische Angaben
- Autor: Heinz Hanßmann
- 2006, 242 Seiten, 22 Schwarz-Weiß-Abbildungen, Maße: 15,7 x 23,6 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 354038894X
- ISBN-13: 9783540388944
- Erscheinungsdatum: 05.10.2006
Sprache:
Englisch
Rezension zu „Hanßmann, H: Local and Semi-Local Bifurcations “
From the reviews:"This book deals with bifurcations of invariant tori in Hamiltonian systems, in particular in near-integrable systems. ... The book closes with a series of appendices, in which technical or more fundamental details are summarised ... . This well-written monograph represents a welcome contribution to the literature in this field-I am not aware of a similarly comprehensive and systematic treatment of bifurcations of invariant tori. I recommend the book to any researchers or graduate students working in this field." (Thomas Wagenknecht, Mathematical Reviews, Issue 2008 a)
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