An algorithmic view of pseudochaos

The controversial concept of quantum chaos - the dynamical chaos in bounded mesoscopic quantum systems - is presented as the most important and universal instance of a new generic dynamical phenomenon: pseudochaos. The latter characterizes the irregular behaviour of dynamical systems with discrete energy and/or frequency spectrum, which include classical systems with discrete phase space. The question of randomness is addressed in terms of the algorithmic theory of dynamical systems, using the Arnold cat map for illustration. The relationship between the algorithmic theory and ergodic theory is discussed. (C) 1999 Elsevier Science B.V. All rights reserved.