Editing Orbit (dynamics) (section)

{{Short description|Set of points linked through the evolution function of a dynamical system}}
{{About|orbits in dynamical systems theory||Orbit (disambiguation)}}
{{no footnotes|date=February 2013}}

In [[mathematics]], specifically in the study of [[dynamical system]]s, 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 (dynamical system)|phase space]] covered by the trajectory of the dynamical system under a particular set of [[initial condition]]s, as the system evolves. As a phase space trajectory is uniquely determined for any given set of phase space coordinates, it is not possible for different orbits to intersect in phase space, therefore the set of all orbits of a dynamical system is a [[partition (set theory)|partition]] of the phase space. Understanding the properties of orbits by using [[Topological dynamics|topological methods]] is one of the objectives of the modern theory of dynamical systems.  

For [[discrete-time dynamical system]]s, the orbits are [[sequence]]s; for [[real dynamical system]]s, the orbits are [[curve]]s; and for [[holomorphic function|holomorphic]] dynamical systems, the orbits are [[Riemann surface]]s.