Overview
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.
Full Product Details
Author: Heinz Hanßmann
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 2007 ed.
Volume: 1893
Dimensions:
Width: 15.50cm
, Height: 1.40cm
, Length: 23.50cm
Weight: 0.454kg
ISBN: 9783540388944
ISBN 10: 354038894
Pages: 242
Publication Date: 05 October 2006
Audience:
College/higher education
,
Undergraduate
Format: Paperback
Publisher's Status: Active
Availability: Out of print, replaced by POD
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Reviews
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)
"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)"
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)
