Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems, invariant measures, numerical examples, algorithm, Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.), Attractors and repellers of smooth dynamical systems and their topological structure, attractors, adaptive subdivision technique, dynamical systems, Entropy and other invariants, isomorphism, classification in ergodic theory, Numerical nonlinear stabilities in dynamical systems, box refinement