Chaotic and stochastic phenomena in systems with non-invertible non-linearities

We show that systems with non-invertible non-linearities can produce sequences of deterministically independent values. We present autonomous dynamical systems that exhibit random behavior in such a way that all variables (taken separately) are unpredictable. We study a new mechanism for chaos in which a static system without inertial or dynamical elements can produce complexity. Using some results of exactly solvable chaotic systems we investigate the influence of different chaotic signals on the phenomenon of stochastic resonance. We report the results of real experiments concerning all these phenomena.