Some characteristics of complex behavior of orbits in dynamical systems

We present a brief review of mathematical notions of complexity based on instability of orbits. We show that the complexity as a function of time may grow exponentially in chaotic situations or polynomially for systems with zero topological entropy. At the end we discuss the class of nonchaotic systems for which all orbits are stable but nevertheless behavior of orbits is complex. We introduce a new notion of complexity for such a kind of systems.