Topological Approach to Rigorous Numerics of Chaotic Dynamical Systems with Strong Expansion of Error Bounds
A new algorithm for obtaining rigorous results concerning the existence of chaotic invariant sets of dynamical systems generated by non-autonomous, time-periodic differential equations is presented. Unlike all other algorithms the presented algorithm does not require the numerical integration of the solutions and as a consequence it is insensitive to the rapid error growth in the case of long integration. The result is based on a new theoretical approach to the computation of the homology of the Poincar, map. A concrete numerical example concerning a time-periodic differential equation in the complex plane is provided.
poincare map fixed point index isolating block symbolic dynamics interval arithmetic rigorous numerical algorithm