ENGLISH

Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems

By Heinz Hanβmann (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2007
ISBN
978-3-540-38894-4, 978-3-540-38896-8
DOI
10.1007/3-540-38894-X
Language
english
Format
PDF
Filesize
9 MB (9494502 bytes)
Series
Lecture Notes in Mathematics 1893
Edition
1
Pages
242\247
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Dynamical Systems and Ergodic Theory;Ordinary Diff

Description

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.

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