Dynamical System
The theory of dynamical systems is a major mathematical discipline closely intertwined with most of the main areas of mathematics, for example, analysis, geometry, differential equations etc. Its mathematical core is the study of the global orbit structure of maps and flows with emphasis on properties invariant under coordinate changes. Its concepts, methods, and paradigms greatly stimulate research in many sciences and have given rise to the vast new areas of applied dynamics (also called nonlinear science or chaos theory).
The fields of dynamical systems comprises several major disciplines, but we are interested mainly in dynamics of holomorphic maps, arithmetic properties of dynamical systems, Teichmuller flows and algebraic geometry, celestial mechanics and differential equations, with many other interesting applications.

The theory of dynamical systems is a major mathematical discipline closely intertwined with most of the main areas of mathematics, for example, analysis, geometry, differential equations etc. Its mathematical core is the study of the global orbit structure of maps and flows with emphasis on properties invariant under coordinate changes. Its concepts, methods, and paradigms greatly stimulate research in many sciences and have given rise to the vast new areas of applied dynamics (also called nonlinear science or chaos theory).
The fields of dynamical systems comprises several major disciplines, but we are interested mainly in dynamics of holomorphic maps, arithmetic properties of dynamical systems, Teichmuller flows and algebraic geometry, celestial mechanics and differential equations, with many other interesting applications.