REVERSING SYMMETRIES IN DYNAMIC-SYSTEMS

Dynamical systems may possess, in addition to symmetries that leave the equations of motion invariant, reversing symmetries that invert the equations of motion. Such dynamical systems are called (weakly) reversible. Some consequences of the existence of reversing symmetries for dynamical systems with discrete time (mappings) are discussed. A reversing symmetry group is introduced and it is shown that every (weakly) reversible mapping L can be decomposed into two mappings K0 and K1 of the same order 2l (limit l --> infinity included) such that K0(2)o K1(2) = I. Some applications are discussed briefly.