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.

In these notes, we review some fundamental concepts and results in the theory of dynamical systems with an emphasis on diferentiable dynamics.

Dec 3, 2025 · Technically, a dynamical system is a smooth action of the reals or the integers on another object (usually a manifold). When the reals are acting, the system is called a continuous dynamical …

Definition: Dynamical System A dynamical system is a system whose state is uniquely specified by a set of variables and whose behavior is described by predefined rules.

Jul 4, 2010 · We first give an abstract and general definition of a dynamical system, which will then be given a more concrete content in the form of a number of specific classes of dynamical systems.

Dynamical systems are constructions that capture the evolution of mathematical structures over time. Modern research in the study of dynamical systems includes the exploration of questions of a purely …

A dynamical system is a mathematical formalization for any fixed rule which describes the dependence of a point’s position in some ambient space on a parameter.

Jun 14, 2025 · Dynamical systems are mathematical models that describe the time-evolution of a system. They are used to study a wide range of phenomena in science and engineering, from simple …

First, we define a dynamical system and give several examples, including symbolic dynamics. Then we introduce the notions of orbits, invariant sets, and their stability.

Dynamical Systems are mathematical models used to describe and analyze the behavior of complex systems or objects over time. They are composed of multiple elements that interact with one another …