Phase space geometry and stochasticity thresholds in Hamiltonian dynamics

2000 ◽  
Vol 62 (5) ◽  
pp. 6078-6081 ◽  
Author(s):  
Monica Cerruti-Sola ◽  
Marco Pettini ◽  
E. G. D. Cohen
Keyword(s):  
Phase Space ◽  
Hamiltonian Dynamics ◽  
Space Geometry ◽  
Phase Space Geometry

Phase space geometry of constrained systems

1995 ◽  
Vol 105 (3) ◽  
pp. 1539-1545 ◽  
Author(s):  
V. P. Pavlov ◽  
A. O. Starinetz
Keyword(s):  
Phase Space ◽  
Constrained Systems ◽  
Space Geometry ◽  
Phase Space Geometry

Catastrophes with indeterminate outcome

1991 ◽  
Vol 432 (1884) ◽  
pp. 113-123 ◽  
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Invariant Manifolds ◽  
Space Geometry ◽  
Dissipative Dynamical System ◽  
Forced Oscillators ◽  
Phase Space Geometry

A catastrophe in a dissipative dynamical system which causes an attractor to completely lose stability will result in a transient trajectory making a rapid jump in phase space to some other attractor. In systems where more than one other attractor is available, the attractor chosen may depend very sensitively on how the catastrophe is realized. Two examples in forced oscillators of Duffing type illustrate how the probabilities of different outcomes can be estimated using the phase space geometry of invariant manifolds.

Effects of the mean-field dynamics and the phase-space geometry on the cluster formation

1997 ◽  
Vol 624 (3) ◽  
pp. 472-494 ◽  
Author(s):  
Z. Basrak ◽  
Ph. Eudes ◽  
P. Abgrall ◽  
F. Haddad ◽  
F. Sébille
Keyword(s):  
Phase Space ◽  
Cluster Formation ◽  
Mean Field ◽  
Space Geometry ◽  
Phase Space Geometry ◽  
The Mean
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