Definition:Cycle


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


 * 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.