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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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IV.14 Dynamics

Bodil Branner

1 Introduction

Dynamical systems are used to describe the way systems evolve in time, and have their origin in the laws of nature that NEWTON [VI. 14] formulated in Principia Mathematica (1687). The associated mathematical discipline, the theory of dynamics, is closely related to many parts of mathematics, in particular analysis, topology, measure theory, and combinatorics. It is also highly influenced and stimulated by problems from the natural sciences, such as celestial mechanics, hydrodynamics, statistical mechanics, meteorology, and other parts of mathematical physics, as well as reaction chemistry, population dynamics, and economics.

Computer simulations and visualizations play an important role in the development ...

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