dynamical system
A dynamical system on where is an open subset of is a differentiable map
where
satisfies
-
i
for all (the identity function)
-
ii
for all (composition)
Note that a planar dynamical system is the same definition as above but with an open subset of .
References
- HSD Hirsch W. Morris, Smale, Stephen, Devaney L. Robert: Differential Equations, 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 | Bifurcation |
Related topic | ChaoticDynamicalSystem |
Related topic | IndexOfCategories |
Defines | planar dynamical system |