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  2. Dynamical system - Wikipedia

    en.wikipedia.org/wiki/Dynamical_system

    A real dynamical system, real-time dynamical system, continuous time dynamical system, or flow is a tuple (T, M, Φ) with T an open interval in the real numbers R, M a manifold locally diffeomorphic to a Banach space, and Φ a continuous function. If Φ is continuously differentiable we say the system is a differentiable dynamical system.

  3. Dynamical systems theory - Wikipedia

    en.wikipedia.org/wiki/Dynamical_systems_theory

    Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems .

  4. Complex dynamics - Wikipedia

    en.wikipedia.org/wiki/Complex_dynamics

    Complex dynamics, or holomorphic dynamics, is the study of dynamical systems obtained by iterating a complex analytic mapping. This article focuses on the case of algebraic dynamics, where a polynomial or rational function is iterated. In geometric terms, that amounts to iterating a mapping from some algebraic variety to itself.

  5. Markov odometer - Wikipedia

    en.wikipedia.org/wiki/Markov_Odometer

    In mathematics, a Markov odometer is a certain type of topological dynamical system.It plays a fundamental role in ergodic theory and especially in orbit theory of dynamical systems, since a theorem of H. Dye asserts that every ergodic nonsingular transformation is orbit-equivalent to a Markov odometer.

  6. List of dynamical systems and differential equations topics

    en.wikipedia.org/wiki/List_of_dynamical_systems...

    This is a list of dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics, list of equations.

  7. Stability theory - Wikipedia

    en.wikipedia.org/wiki/Stability_theory

    An autonomous system ′ =, where x(t) ∈ R n and A is an n×n matrix with real entries, has a constant solution = (In a different language, the origin 0 ∈ R n is an equilibrium point of the corresponding dynamical system.)

  8. Orbit (dynamics) - Wikipedia

    en.wikipedia.org/wiki/Orbit_(dynamics)

    In mathematics, specifically in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system. It can be understood as the subset of phase space covered by the trajectory of the dynamical system under a particular set of initial conditions, as the system evolves.

  9. Symbolic dynamics - Wikipedia

    en.wikipedia.org/wiki/Symbolic_dynamics

    In mathematics, symbolic dynamics is the study of dynamical systems defined on a discrete space consisting of infinite sequences of abstract symbols. The evolution of the dynamical system is defined as a simple shift of the sequence. Because of their explicit, discrete nature, such systems are often relatively easy to characterize and understand.