FLUCTUATIONS OF LYAPUNOV VECTORS IN LARGE-VOLUME LIMIT AND THE INFORMATION-FLOW CONFIGURATION IN SPACE-TIME DYNAMICS

The fluctuation of Lyapunov vectors in R'' for large n and in the infi nite-dimensional limit are studied in the context of entropy balance f rom dynamical system theory. The density of the fluctuation yields the information-flow configuration (IFC) which captures the interaction o f degrees-of-freedom (DOF) in information-flow terms. Generally, the I FC can be extended or localized. The study of these cases leads to the local formulation of entropy balance for a DOE Two examples of couple d map lattice are given to demonstrate the approach. Based on the nume rical data, we conjecture that a locally balance !imbalance) configura tion of the extended (localized) IFC implies absence (presence) of ''p attern'' in the spatially extended system. Moreover, for dissipative d ynamics, the localization for the largest and smallest exponents can t ake place in a fixed spatial domain, which describes a stronger versio n fluctuation-dissipation principle derived by Ruelle (1982) in viscou s turbulence flow. Some of its implications are discussed.