The Monte-Carlo integration of cylindrical phase-space with leading particles

1989 ◽  
Vol 56 (2) ◽  
pp. 165-180 ◽  
Author(s):  
Vaclav Vrba
Keyword(s):  
Monte Carlo ◽  
Phase Space ◽  
Monte Carlo Integration ◽  
Cylindrical Phase ◽  
Cylindrical Phase Space

FRACTALS AND CLOSURES OF LINEAR DYNAMICAL SYSTEMS EXCITED STOCHASTICALLY BY TEMPORAL INPUTS

2001 ◽  
Vol 11 (03) ◽  
pp. 755-779 ◽  
Author(s):  
RYOICHI WADA ◽  
KAZUTOSHI GOHARA
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Vector Fields ◽  
Invariant Set ◽  
Poincaré Section ◽  
Poincare Section ◽  
Linear Dynamical Systems ◽  
Cylindrical Phase ◽  
Iterated Functions ◽  
Cylindrical Phase Space

Fractals and closures of two-dimensional linear dynamical systems excited by temporal inputs are investigated. The continuous dynamics defined by the set of vector fields in the cylindrical phase space is reduced to the discrete dynamics defined by the set of iterated functions on the Poincaré section. When all iterated functions are contractions, it has already been shown theoretically that a trajectory in the cylindrical phase space converges into an attractive invariant set with a fractal-like structure. Calculating analytically the Lipschitz constants of iterated functions, we show that, under some conditions, noncontractions often appear. However, we numerically show that, even for noncontractions, an attractive invariant set with a fractal-like structure exists. By introducing the interpolating system, we can also show that the set of trajectories in the cylindrical phase space is enclosed by the tube structure whose initial set is the closure of the fractal set on the Poincaré section.

First-Kind Cycles of Systems with Cylindrical Phase Space

2020 ◽  
Vol 248 (4) ◽  
pp. 457-466
Author(s):  
S. S. Mamonov ◽  
A. O. Kharlamova
Keyword(s):  
Phase Space ◽  
Cylindrical Phase ◽  
Cylindrical Phase Space
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