/sci/ - Science & Math

>>11561966
It's the study of maps of the form [math]\phi: T\times M \to M[/math], where [math]T[/math] is an ordered monoid such as [math]\mathbb Z_{\geq 0}[/math], [math]\mathbb R_+[/math] or [math]\mathbb R[/math], and [math]M[/math] is a manifold (or more generally a non-empty set). Here [math]T[/math] is thought of as the "time" and [math]M[/math] as the "state space" of the system. This allows one to use analytical and geometric tools to study discrete systems such as
[eqn]f_{n+2} = f_{n+1} + f_n, ~~ f_1 = 1, ~~ f_0 = 0,[/eqn]
as well as continuous systems such as the ODE
[eqn]x' = f(t,x),[/eqn]
under an unified framework (even though discrete and continuous systems will have their own unique phenomena due to the fact that [math]\mathbb Z \neq \mathbb R[/math]).
https://en.wikipedia.org/wiki/Dynamical_system_(definition)