Pseudochaos

A family of the billiard-type systems with zero Lyapunov exponent is considered as an example of dynamics which is between the regular one and chaotic mixing. This type of dynamics is called ``pseudochaos''. We demonstrate how the fractional kinetic equation can be introduced for the pseudochaos and how the main critical exponents of the fractional kinetics can be evaluated from the dynamics. Problems related to pseudochaos are discussed: Poincare recurrences, continued fractions, log-periodicity, rhombic billiards, and others. Pseudochaotic dynamics and fractional kinetics can be applied to streamlines or magnetic field lines behavior.