Lyapunov spectra of periodic orbits for a many-particle system

Abstract

The Lyapunov spectrum corresponding to a periodic orbit for a two dimensional many particle system with hard core interactions is discussed. Noting that the matrix to describe the tangent space dynamics has the block cyclic structure, the calculation of the Lyapunov spectrum is attributed to the eigenvalue problem of a 16x16 reduced matrices regardless of the number of particles. We show that there is the thermodynamic limit of the Lyapunov spectrum in this periodic orbit. The Lyapunov spectrum has a step structure, which is explained by using symmetries of the reduced matrices.

16 pages, 4 incorporated postscript figures

Cited by in corpus (15)

• Boundary effects in the stepwise structure of the Lyapunov spectra for quasi-one-dimensional systems
• Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems
• Time-oscillating Lyapunov modes and auto-correlation functions for quasi-one-dimensional systems
• Hard Disks in Narrow Channels
• Covariant Lyapunov vectors for rigid disk systems
• Time-dependent mode structure for Lyapunov vectors as a collective movement in quasi-one-dimensional systems
• Master equation approach to the conjugate pairing rule of Lyapunov spectra for many-particle thermostatted systems
• What does dynamical systems theory teach us about fluids?
• Hopping dynamics for localized Lyapunov vectors in many-hard-disk systems
• Lyapunov Modes for a Nonequilibrium System with a Heat Flux
• From Lyapunov modes to the exponents for hard disk systems
• Lyapunov Modes and Time-Correlation Functions for Two-Dimensional Systems
• One dimensional Brownian motion in hard rods: adiabatic piston problem
• Lyapunov modes in three-dimensional Lennard-Jones fluids
• Equivalence of kinetic-theory and random-matrix approaches to Lyapunov spectra of hard-sphere systems