Computing complete Lyapunov functions for discrete-time dynamical systems

A complete Lyapunov function characterizes the behaviour of a general discrete-time dynamical system. In particular, it divides state space into chain-recurrent set where is constant along trajectories and part flow gradient-like strictly decreasing solutions. Moreover, level sets provide information about attractors, repellers, basins attraction. style='text-indent:20px;'>We propose two novel classes methods to compute functions for system given by an iteration. The first class computes approximating solution ill-posed equation its discrete orbital derivative using meshfree collocation. second as minimization problem in reproducing kernel Hilbert space. We apply both several examples.