dynamical system

A dynamical systemMathworldPlanetmathPlanetmath on X where X is an open subset of n is a differentiable map





  • i

    ϕ0(𝐱)=𝐱 for all 𝐱X (the identity function)

  • ii

    ϕtϕs(𝐱)=ϕt+s(𝐱) for all s,t (composition)


Note that a planar dynamical system is the same definition as above but with X an open subset of 2.


  • HSD Hirsch W. Morris, Smale, Stephen, Devaney L. Robert: Differential EquationsMathworldPlanetmath, Dynamical Systems & An Introduction to Chaos (Second Edition). Elsevier Academic Press, New York, 2004.
  • PL Perko, Lawrence: Differential Equations and Dynamical Systems (Third Edition). Springer, New York, 2001.
Title dynamical system
Canonical name DynamicalSystem
Date of creation 2013-03-22 14:06:25
Last modified on 2013-03-22 14:06:25
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 14
Author PrimeFan (13766)
Entry type Definition
Classification msc 34-00
Classification msc 37-00
Synonym supercategorical dynamics
Related topic SystemDefinitions
Related topic GroupoidCDynamicalSystem
Related topic CategoricalDynamics
Related topic BifurcationMathworldPlanetmath
Related topic ChaoticDynamicalSystem
Related topic IndexOfCategories
Defines planar dynamical system