Overview
All data
7 statements · 14% with external sources · numbers in brackets are citations
- Defining formula
\Phi U \subset T \times M \to M
On other databases
5 identifiers linking dynamical systems across the web's reference databases
7 statements · 14% with external sources · numbers in brackets are citations
\Phi U \subset T \times M \to M 5 identifiers linking dynamical systems across the web's reference databases
From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it.