On numerical approaches to the analysis of topology of the phase space for dynamical integrability

Reference : On numerical approaches to the analysis of topology of the phase space for dynamical ...


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/23196

Title :	On numerical approaches to the analysis of topology of the phase space for dynamical integrability
Language :	English
Author, co-author :	Salnikov, Vladimir [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	2013
Journal title :	Chaos, Solitons & Fractals
Publisher :	Pergamon Press - An Imprint of Elsevier Science
Peer reviewed :	Yes (verified by ORBi^lu)
Audience :	International
ISSN :	0960-0779
Abstract :	[en] In this paper we consider the possibility to use numerical simulations for a computer assisted qualitative analysis of dynamical systems. We formulate a rather general method of recovering the obstructions to dynamical integrability for the systems that after reduction have a small number of degrees of freedom. We generalize this method using the results of KAM theory and stochastic approaches to the families of parameter depending systems. This permits to localize possible integrability regions in the parameter space. We give some examples of application of this approach to dynamical systems having a mechanical origin.
Permalink :	http://hdl.handle.net/10993/23196

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