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A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space.  Small changes in the state of the system correspond to small changes in the numbers.  The numbers are also the coordinates of a geometrical space—a manifold.  The evolution rule of the dynamical system is a fixed rule that describes what future states follow from the current state.  The rule may be deterministic (for a given time interval only one future state follows from the current state) or stochastic (the evolution of the state is subject to random shocks).

A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space.  Small changes in the state of the system correspond to small changes in the numbers.  The numbers are also the coordinates of a geometrical space—a manifold.  The evolution rule of the dynamical system is a fixed rule that describes what future states follow from the current state.  The rule may be deterministic (for a given time interval only one future state follows from the current state) or stochastic (the evolution of the state is subject to random shocks).

动力系统的状态是由一组实数决定的，更广泛地说，是由适当的状态空间中的一组点决定的。系统状态的微小变化对应于数字的变化。这些数字也是几何空间——流形（manifold）——的坐标系（coordinates ）--[[用户:嘉树|嘉树]]（[[用户讨论:嘉树|讨论]]）这里翻译为坐标还是坐标系更好一点？。动力系统的演化是描述了在当前状态之后出现的未来状态的固定规则。这个规则可以是确定性的(在给定的时间间隔内，有且仅有一个未来状态在当前状态之后出现)，或随机性的(状态的演化受到随机因素的影响)。

动力系统的状态是由一组实数决定的，更广泛地说，是由适当的状态空间中的一组点决定的。系统状态的微小变化对应于数字的变化。这些数字也是几何空间——流形（manifold）——的坐标系（coordinates ）--[[用户:嘉树|嘉树]]（[[用户讨论:嘉树|这里翻译为坐标还是坐标系更好一点？]]）。动力系统的演化是描述了在当前状态之后出现的未来状态的固定规则。这个规则可以是确定性的(在给定的时间间隔内，有且仅有一个未来状态在当前状态之后出现)，或随机性的(状态的演化受到随机因素的影响)。

=== Dynamicism 动态主义===

=== Dynamicism 动态主义===