Discrete Dynamical Systems with Symmetries: Computer Analysis

摘要

Discrete dynamical systems and mesoscopic lattice models are considered from the standpoint of their symmetry groups. Universal specific features of deterministic dynamical system behavior associated with nontrivial symmetries of these systems are specified. Group nature of soliton-like moving structures of the "spaceship" type in cellular automata is revealed. Study of lattice models is also considerably simplified when their symmetry groups are taken into account. A program in C for group analysis of systems of both types is developed. The program, in particular, constructs and investigates phase portraits of discrete dynamical systems modulo symmetry group and seeks dynamical systems possessing special features, such as, for example, reversibility. For mesoscopic lattice models, the program computes microcanonical distributions and looks for phase transitions. Some computational results and observations are presented.