TY - GEN
T1 - Theory of stochastic transitions in area preserving maps
AU - Tessarotto, Massimo
AU - Nicolini, Piero
PY - 2005/5/16
Y1 - 2005/5/16
N2 - 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.
AB - 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.
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U2 - 10.1063/1.1941526
DO - 10.1063/1.1941526
M3 - Conference contribution
AN - SCOPUS:33749020796
SN - 0735402477
SN - 9780735402478
T3 - AIP Conference Proceedings
SP - 132
EP - 140
BT - RAREFIED GAS DYNAMICS
T2 - 24th International Symposium on Rarefied Gas Dynamics, RGD24
Y2 - 10 July 2004 through 16 July 2004
ER -