title: Finite-space Lyapunov exponents and pseudochaos.
abstract: We propose a definition of finite-space Lyapunov exponent. For discrete-time dynamical systems, it measures the local (between neighboring points) average spreading of the system. We justify our definition by showing that, for large classes of chaotic maps, the corresponding finite-space Lyapunov exponent approaches the Lyapunov exponent of a chaotic map when M-->infinity, where M is the cardinality of the discrete phase space. In analogy with continuous systems, we say the system has pseudochaos if its finite-space Lyapunov exponent tends to a positive number (or to +infinity), when M-->infinity.
authors.affiliation: Institute for Nonlinear Science University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0402, USA. lkocarev@ucsd.edu
authors.forename: Ljupco
authors.initials: L
authors.lastname: Kocarev
authors.forename: Janusz
authors.initials: J
authors.lastname: Szczepanski