In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.
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- Dynamical systems theory began in the late nineteenth century with the work of Henri Poincaré (1854–1912). He solved an important problem in celestial mechanics by using techniques of dynamical systems. In modern times, Stephen Smale, Adrien Douady, John Milnor, Lennart Carleson, and many other notable mathematicians have helped to develop this theory into a powerful mathematical tool. The subject is exciting in that it integrates analysis, geometry, and computer graphics into a whole that is greater than the sum of its parts.
- Steven G. Krantz; Harold R. Parks (10 May 2014). A Mathematical Odyssey: Journey from the Real to the Complex. Springer. p. 82. ISBN 978-1-4614-8939-9.