Lyapunov characteristic numbers and Kolmogorov entropy of a four-dimensional mapping

1980 ◽  
Vol 55 (1) ◽  
pp. 59-69 ◽  
Author(s):  
C. Froeschlé ◽  
R. Gonczi
Keyword(s):  
Kolmogorov Entropy ◽  
Characteristic Numbers ◽  
Dimensional Mapping ◽  
Lyapunov Characteristic Numbers

scholarly journals On the Measure-Preserving Mappings with Three-Dimensions

1993 ◽  
Vol 132 ◽  
pp. 73-89
Author(s):  
Yi-Sui Sun
Keyword(s):  
Fixed Point ◽  
Invariant Manifolds ◽  
Three Dimensional ◽  
Invariant Curve ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Kolmogorov Entropy ◽  
Numerical Exploration ◽  
Area Preserving ◽  
Dimensional Mapping

AbstractWe have systematically made the numerical exploration about the perturbation extension of area-preserving mappings to three-dimensional ones, in which the fixed points of area preserving are elliptic, parabolic or hyperbolic respectively. It has been observed that: (i) the invariant manifolds in the vicinity of the fixed point generally don’t exist (ii) when the invariant curve of original two-dimensional mapping exists the invariant tubes do also in the neighbourhood of the invariant curve (iii) for the perturbation extension of area-preserving mapping the invariant manifolds can only be generated in the subset of the invariant manifolds of original two-dimensional mapping, (iv) for the perturbation extension of area preserving mappings with hyperbolic or parabolic fixed point the ordered region near and far from the invariant curve will be destroyed by perturbation more easily than the other one, This is a result different from the case with the elliptic fixed point. In the latter the ordered region near invariant curve is solid. Some of the results have been demonstrated exactly.Finally we have discussed the Kolmogorov Entropy of the mappings and studied some applications.

RUELLE'S INEQUALITY FOR ISOTROPIC ORNSTEIN–UHLENBECK FLOWS

2010 ◽  
Vol 10 (01) ◽  
pp. 143-154 ◽  
Author(s):  
HOLGER VAN BARGEN
Keyword(s):  
Dynamical System ◽  
Random Dynamical System ◽  
Characteristic Numbers ◽  
Lyapunov Characteristic Numbers

Ruelle's inequality asserts that the entropy of a dynamical system is bounded from above by the Lyapunov characteristic numbers counted with their multiplicities. We show that this inequality holds true in the case of a random dynamical system deduced from an isotropic Ornstein–Uhlenbeck-flow (IOUF).

scholarly journals Pluto's Lyapunov numbers in different dynamical models

1996 ◽  
Vol 172 ◽  
pp. 71-74 ◽  
Author(s):  
R. Dvorak ◽  
E. Lohinger
Keyword(s):  
Body Problem ◽  
Stable Region ◽  
Three Body Problem ◽  
Orbital Elements ◽  
Dynamical Models ◽  
Characteristic Numbers ◽  
Numerical Integrations ◽  
Lyapunov Numbers ◽  
Three Body ◽  
Lyapunov Characteristic Numbers

We present the results of numerical integrations of Pluto and some fictitious Plutos in three different models (the circular and the elliptic restricted three body problem and the outer solar system). We determined the “extension” of the stable region in these models by means of the Lyapunov Characteristic Numbers and by an analysis of the orbital elements.

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