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=== Arithmetic dynamics ===

=== Arithmetic dynamics 算术动态系统===

:[[Arithmetic dynamics]] is a field that emerged in the 1990s that amalgamates two areas of mathematics, [[dynamical systems]] and [[number theory]]. Classically, discrete dynamics refers to the study of the [[Iterated function|iteration]] of self-maps of the [[complex plane]] or [[real line]]. Arithmetic dynamics is the study of the number-theoretic properties of integer, rational, {{math|<var>p</var>}}-adic, and/or algebraic points under repeated application of a [[polynomial]] or [[rational function]].

:[[Arithmetic dynamics]] is a field that emerged in the 1990s that amalgamates two areas of mathematics, [[dynamical systems]] and [[number theory]]. Classically, discrete dynamics refers to the study of the [[Iterated function|iteration]] of self-maps of the [[complex plane]] or [[real line]]. Arithmetic dynamics is the study of the number-theoretic properties of integer, rational, {{math|<var>p</var>}}-adic, and/or algebraic points under repeated application of a [[polynomial]] or [[rational function]].

=== Projected dynamical systems 投影动力系统===

=== Projected dynamical systems ===

:[[Projected dynamical systems]] it is a [[mathematics|mathematical]] theory investigating the behaviour of [[dynamical system]]s where solutions are restricted to a constraint set. The discipline shares connections to and applications with both the static world of [[Optimization (mathematics)|optimization]] and [[Equilibrium point|equilibrium]] problems and the dynamical world of [[ordinary differential equations]]. A projected dynamical system is given by the [[flow (mathematics)|flow]] to the projected differential equation.

:[[Projected dynamical systems]] it is a [[mathematics|mathematical]] theory investigating the behaviour of [[dynamical system]]s where solutions are restricted to a constraint set. The discipline shares connections to and applications with both the static world of [[Optimization (mathematics)|optimization]] and [[Equilibrium point|equilibrium]] problems and the dynamical world of [[ordinary differential equations]]. A projected dynamical system is given by the [[flow (mathematics)|flow]] to the projected differential equation.

Projected dynamical systems it is a mathematical theory investigating the behaviour of dynamical systems where solutions are restricted to a constraint set. The discipline shares connections to and applications with both the static world of optimization and equilibrium problems and the dynamical world of ordinary differential equations. A projected dynamical system is given by the flow to the projected differential equation.

Projected dynamical systems it is a mathematical theory investigating the behaviour of dynamical systems where solutions are restricted to a constraint set. The discipline shares connections to and applications with both the static world of optimization and equilibrium problems and the dynamical world of ordinary differential equations. A projected dynamical system is given by the flow to the projected differential equation.

=== Symbolic dynamics ===

=== Symbolic dynamics 符号动力学===

:[[Symbolic dynamics]] is the practice of modelling a topological or smooth [[dynamical system]] by a discrete space consisting of infinite [[sequence]]s of abstract symbols, each of which corresponds to a state of the system, with the dynamics (evolution) given by the [[shift operator]].

:[[Symbolic dynamics]] is the practice of modelling a topological or smooth [[dynamical system]] by a discrete space consisting of infinite [[sequence]]s of abstract symbols, each of which corresponds to a state of the system, with the dynamics (evolution) given by the [[shift operator]].

Symbolic dynamics is the practice of modelling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which corresponds to a state of the system, with the dynamics (evolution) given by the shift operator.

Symbolic dynamics is the practice of modelling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which corresponds to a state of the system, with the dynamics (evolution) given by the shift operator.

符号动力学是通过一个由无限抽象符号序列组成的离散空间建立一个拓扑或光滑动力系统的实践，每一个抽象符号序列对应于一个系统的状态，由移位算子给出动力学(演化)。

符号动力学是通过一个由抽象符号的无限序列组成的离散空间建立一个拓扑或光滑动力系统的实践。每一个抽象符号的无限序列序列对应于系统的一个状态，并由移位算子给出动力学(演化)。

=== System dynamics ===

=== System dynamics 系统动力学===

:[[System dynamics]] is an approach to understanding the behaviour of systems over time.  It deals with internal feedback loops and time delays that affect the behaviour and state of the entire system.<ref name="sysdyn">[http://sysdyn.clexchange.org MIT System Dynamics in Education Project (SDEP)<!-- Bot generated title -->] {{webarchive|url=https://web.archive.org/web/20080509163801/http://sysdyn.clexchange.org/ |date=2008-05-09 }}</ref>  What makes using system dynamics different from other approaches to studying systems is the use of [[feedback]] loops and [[Stock and flow|stocks and flows]].  These elements help describe how even seemingly simple systems display baffling [[nonlinearity]].

:[[System dynamics]] is an approach to understanding the behaviour of systems over time.  It deals with internal feedback loops and time delays that affect the behaviour and state of the entire system.<ref name="sysdyn">[http://sysdyn.clexchange.org MIT System Dynamics in Education Project (SDEP)<!-- Bot generated title -->] {{webarchive|url=https://web.archive.org/web/20080509163801/http://sysdyn.clexchange.org/ |date=2008-05-09 }}</ref>  What makes using system dynamics different from other approaches to studying systems is the use of [[feedback]] loops and [[Stock and flow|stocks and flows]].  These elements help describe how even seemingly simple systems display baffling [[nonlinearity]].

System dynamics is an approach to understanding the behaviour of systems over time.  It deals with internal feedback loops and time delays that affect the behaviour and state of the entire system.  What makes using system dynamics different from other approaches to studying systems is the use of feedback loops and stocks and flows.  These elements help describe how even seemingly simple systems display baffling nonlinearity.

System dynamics is an approach to understanding the behaviour of systems over time.  It deals with internal feedback loops and time delays that affect the behaviour and state of the entire system.  What makes using system dynamics different from other approaches to studying systems is the use of feedback loops and stocks and flows.  These elements help describe how even seemingly simple systems display baffling nonlinearity.

=== Topological dynamics ===

=== Topological dynamics 拓扑动力学===

:[[Topological dynamics]] is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of [[general topology]].

:[[Topological dynamics]] is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of [[general topology]].

Topological dynamics is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of general topology.

Topological dynamics is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of general topology.

== Applications ==

== Applications ==