Jeroen S.W. Lamb:

Reversing symmetries in dynamical systems

abstract:

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 {\em (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 $K_0$ and $K_1$ of
the same order $2^l$ (limit $l\rightarrow\infty$ included) such that 
$K_0^2\circ K_1^2=I$.
Some applications are discussed briefly.