Title: Lyapunov modes in extended systems
Abstract:
Lyapunov analysis deals with the
behavior of small perturbations of trajectories of general dynamical
systems. While the growth or decay strength of such perturbations, as
described by the spectrum of Lyapunov exponents, has been
investigated in detail, it was only recently that the associated
directions in state space, the Lyapunov vectors, came into the focus
of the scientific community. They are the generalization of normal
modes of harmonic systems to nonlinear, chaotic systems. The interest
was triggered by the observation that some of these vectors may
exhibit long wavelength, low frequency behavior similar to that of
classical hydrodynamic modes. In this contribution we discuss mayor
aspects of these hydrodynamic Lyapunov modes (HLM) for Hamiltonian
and dissipative systems, and also more recent findings about the role
of so-called covariant Lyapunov vectors (CLV) in determining the
effective number of degrees of freedom of extended systems.
Keywords: ?