Strange nonchaotic attractors

Aperiodic dynamics which is nonchaotic is realized on Strange Nonchaotic At tractors (SNAs). Such attractors are generic in quasiperiodically driven no nlinear systems, and like strange attractors, are geometrically fractal. Th e largest Lyapunov exponent is zero or negative: trajectories do not show e xponential sensitivity to initial conditions. In recent years, SNAs have be en seen in a number of diverse experimental situations ranging from quasipe riodically driven mechanical or electronic systems to plasma discharges. An important connection is the equivalence between a quasiperiodically driven system and the Schrodinger equation for a particle in a related quasiperio dic potential, showing a correspondence between the localized states of the quantum problem with SNAs in the related dynamical system. In this review we discuss the main conceptual issues in the study of SNAs, including the d ifferent bifurcations or routes for the creation of such attractors, the me thods of characterization, and the nature of dynamical transitions in quasi periodically forced systems. The variation of the Lyapunov exponent, and th e qualitative and quantitative aspects of its local fluctuation properties, have emerged as an important means of studying fractal attractors, and thi s analysis finds useful application here. The ubiquity of such attractors, in conjunction with their several unusual properties, suggests novel applic ations.