p-adic discrete dynamical systems and their applications in physics and cognitive sciences

This survey is devoted to dynamical systems on fields of p-adic numbers. We discuss the origin of p-adic dynamics in p-adic theoretical physics (string theory, quantum mechanics and field theory, spin glasses), continuous dynamical systems, and discrete dynamical systems. The main attention is paid to discrete dynamical systems, especially to iterations of mappings on the field of p-adic numbers (or their algebraic extensions); we discuss ergodicity problems, the behavior of cycles, holomorphic dynamics, and applications of p-adic discrete dynamical systems to cognitive sciences and psychology.