Poincaré cycles of a many-particle system are exemplified by the motion of a linear chain. It is shown that the recurrence time increases in an approximately exponential way with the number of degrees of freedom, and as a power of the sharpness with which the recurrent state is specified. An explicit formula is given which is applicable to other separable dynamical systems as well.

• Received 21 January 1958

DOI:https://doi.org/10.1103/PhysRev.111.689