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20210702081523.0 |
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|a 9783540388968
|9 978-3-540-38896-8
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|a 10.1007/3-540-38894-X
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|a Hanßmann, Heinz.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems
|h [electronic resource] :
|b Results and Examples /
|c by Heinz Hanßmann.
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|a 1st ed. 2007.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg :
|b Imprint: Springer,
|c 2007.
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|a XVI, 242 p. 22 illus.
|b online resource.
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|a text
|b txt
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|a computer
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|a online resource
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|a text file
|b PDF
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1893
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| 505 |
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|a 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.
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|a 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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|a Dynamics.
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|a Ergodic theory.
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|a Differential equations.
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|a Global analysis (Mathematics).
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|a Manifolds (Mathematics).
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|a Mathematical physics.
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|a Dynamical Systems and Ergodic Theory.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
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|a Ordinary Differential Equations.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M12147
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|a Global Analysis and Analysis on Manifolds.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M12082
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|a Theoretical, Mathematical and Computational Physics.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/P19005
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|a SpringerLink (Online service)
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|t Springer Nature eBook
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|i Printed edition:
|z 9783540828662
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| 776 |
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|i Printed edition:
|z 9783540388944
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| 830 |
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1893
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|u https://doi.org/10.1007/3-540-38894-X
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|a ZDB-2-LNM
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|a Mathematics and Statistics (SpringerNature-11649)
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|a Mathematics and Statistics (R0) (SpringerNature-43713)
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