Definition:Cycle


 * Cycle (group theory): A permutation $\rho$ such that $\rho^k \left({i}\right) = i$ and $\rho$ fixes each $j$ not in $\left\{{i, \rho \left({i}\right), \ldots, \rho^{k-1} \left({i}\right)}\right\}$.
 * Also see Cycle notation.


 * Cycle (graph theory): A circuit in which no vertex except the first appears more than once.


 * Cycle (Periodic Solution): A solution of a differential equation which is a periodic function.