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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system. The orbit is a subset of the phase space and the set of all orbits is a partition of the phase space, that is different orbits do not intersect in the phase space. Understanding the properties of orbits by using topological method is one of the objectives of the modern theory of dynamical systems. For discrete-time dynamical systems the orbits are sequences, for real dynamical systems the orbits are curves and for holomorphic dynamical systems the orbits are Riemann surfaces.