scholarly journals On the Lyapunov numbers

2013 ◽  
Vol 131 (2) ◽  
pp. 209-218 ◽  
Author(s):  
Sergiĭ Kolyada ◽  
Oleksandr Rybak
Keyword(s):  
Lyapunov Numbers

scholarly journals Chaos and Its Impact on the Foundations of Statistical Mechanics

1996 ◽  
Vol 49 (1) ◽  
pp. 51 ◽  
Author(s):  
Gary P Morriss ◽  
Lamberto Rondoni
Keyword(s):  
Periodic Orbit ◽  
Lorentz Gas ◽  
Analytic Formula ◽  
Numerical Techniques ◽  
Lyapunov Numbers ◽  
Statistical Mechanical Model ◽  
Statistical Mechanical ◽  
Definition Of ◽  
Dynamics Simulations ◽  
Good Agreement

In this work we present a brief derivation of the periodic orbit expansion for simple dynamical systems, and then we apply it to the study of a classical statistical mechanical model, the Lorentz gas, both at equilibrium and in a nonequilibrium steady state. The results are compared with those obtained through standard molecular dynamics simulations, and they are found to be in good agreement. The form of the average using the periodic orbit expansion suggests the definition of a new dynamical partition function, which we test numerically. An analytic formula is obtained for the Lyapunov numbers of periodic orbits for the nonequilibrium Lorentz gas. Using this formula and other numerical techniques we study the nonequilibrium Lorentz gas as a dynamical system and obtain an estimate of the upper bound on the external field for which the system remains ergodic.

Spectra and Lyapunov Numbers in Pulsating Systemsa

1995 ◽  
Vol 773 (1) ◽  
pp. 189-204 ◽  
Author(s):  
HAYWOOD SMITH ◽  
GEORGE CONTOPOULOS
Keyword(s):  
Lyapunov Numbers

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.

scholarly journals The Lyapunov dimension of a nowhere differentiable attracting torus

1984 ◽  
Vol 4 (2) ◽  
pp. 261-281 ◽  
Author(s):  
James L. Kaplan ◽  
John Mallet-Paret ◽  
James A. Yorke
Keyword(s):  
Fractal Dimension ◽  
Lyapunov Dimension ◽  
Lyapunov Numbers

AbstractThe fractal dimension of an attracting torus Tk in × Tk is shown to be almost always equal to the Lyapunov dimension as predicted by a previous conjecture. The cases studied here can have several Lyapunov numbers greater than 1 and several less than 1

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