Dynamical Systems and Chaos

Abstract

A dynamical system is a mathematical object to describe the development of a physical, biological or another system from real life depending on time. It is defined by a phase space M, and by a one parameter family of map**s φ ^t: M → M, where t is the parameter (the time). In the following discussion the phase space is often $\text{I}\!\!\text{R}^{n}$, a subset of it, or a metric space.