Editing Dynamical system (section)

==== Real dynamical system ====
A ''real dynamical system'', ''real-time dynamical system'', ''[[continuous time]] dynamical system'', or ''[[Flow (mathematics)|flow]]'' is a tuple (''T'', ''M'', Φ) with ''T'' an [[open interval]] in the [[real number]]s '''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''.  If the manifold ''M'' is locally diffeomorphic to '''R'''<sup>''n''</sup>, the dynamical system is ''finite-dimensional''; if not, the dynamical system is ''infinite-dimensional''. This does not assume a [[symplectic manifold|symplectic structure]]. When ''T'' is taken to be the reals, the dynamical system is called ''global'' or a ''[[Flow (mathematics)|flow]]''; and if ''T'' is restricted to the non-negative reals, then the dynamical system is a ''semi-flow''.