Boundary effects in the stepwise structure of the Lyapunov spectra for quasi-one-dimensional systems.
Boundary effects in the stepwise structure of the Lyapunov spectra and corresponding wavelike structure of the Lyapunov vectors are discussed numerically in quasi-one-dimensional systems of many hard disks. Four different types of boundary conditions are constructed by combinations of periodic boundary conditions and hard-wall boundary conditions, and each leads to different stepwise structures of the Lyapunov spectra. We show that for some Lyapunov exponents in the step region, the spatial y component of the corresponding Lyapunov vector deltaq(yj), divided by the y component of momentum p(yj), exhibits a wavelike structure as a function of position q(xj) and time t. For the other Lyapunov exponents in the step region, the y component of the corresponding Lyapunov vector deltaq(yj) exhibits a time-independent wavelike structure as a function of q(xj). These two types of wavelike structure are used to categorize the type and sequence of steps in the Lyapunov spectra for each different type of boundary condition.
Taniguchi
Tooru
T
School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia.
Morriss
Gary P
GP