Theory of stochastic transitions in area preserving maps

Massimo Tessarotto, Piero Nicolini

Research output: Chapter in Book/Report/Conference proceedingConference contribution


A famous aspect of discrete dynamical systems defined by area-preserving maps is the physical interpretation of stochastic transitions occurring locally which manifest themselves through the destruction of invariant KAM curves and the local or global onset of chaos. Despite numerous previous investigations (see in particular Chirikov, Greene, Percival, Escande and Doveil and MacKay) based on different approaches, several aspects of the phenomenon still escape a complete understanding and a rigorous description. In particular Greene's approach is based on several conjectures, one of which is that the stochastic transition leading to the destruction of the last KAM curve in the standard map is due the linear destabilization of the elliptic points belonging to a peculiar family of invariants sets I(m,n) (rational iterates) having rational winding numbers and associated to the last KAM curve. Purpose of this work is to analyze the nonlinear phenomena leading to the stochastic transition in the standard map and their effect on the destabilization of the invariant sets associated to the KAM curves, leading, ultimately, to the destruction of the KAM curves themselves.

Original languageEnglish (US)
Title of host publicationRAREFIED GAS DYNAMICS
Subtitle of host publication24th International Symposium on Rarefied Gas Dynamics, RGD24
Number of pages9
StatePublished - May 16 2005
Event24th International Symposium on Rarefied Gas Dynamics, RGD24 - Bari, Italy
Duration: Jul 10 2004Jul 16 2004

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


Conference24th International Symposium on Rarefied Gas Dynamics, RGD24

ASJC Scopus subject areas

  • General Physics and Astronomy


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