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An attractor is called strange if it has a fractal structure. This is often the case when the dynamics on it are chaotic, but strange nonchaotic attractors also exist.  If a strange attractor is chaotic, exhibiting sensitive dependence on initial conditions, then any two arbitrarily close alternative initial points on the attractor, after any of various numbers of iterations, will lead to points that are arbitrarily far apart (subject to the confines of the attractor), and after any of various other numbers of iterations will lead to points that are arbitrarily close together. Thus a dynamic system with a chaotic attractor is locally unstable yet globally stable: once some sequences have entered the attractor, nearby points diverge from one another but never depart from the attractor.

An attractor is called strange if it has a fractal structure. This is often the case when the dynamics on it are chaotic, but strange nonchaotic attractors also exist.  If a strange attractor is chaotic, exhibiting sensitive dependence on initial conditions, then any two arbitrarily close alternative initial points on the attractor, after any of various numbers of iterations, will lead to points that are arbitrarily far apart (subject to the confines of the attractor), and after any of various other numbers of iterations will lead to points that are arbitrarily close together. Thus a dynamic system with a chaotic attractor is locally unstable yet globally stable: once some sequences have entered the attractor, nearby points diverge from one another but never depart from the attractor.

如果吸引子具有[[分形]]结构，则称为“奇异”。当它的动力学是[[混沌理论|混沌]]时，通常会出现这种情况，但是[[奇异的非混沌吸引子]]也存在。如果一个<font color="#ff8000"> 奇异吸引子</font>是混沌的，表现出[[对初始条件的敏感依赖性]]，那么在吸引子上任意两个任意接近的备选初始点，经过任意多次迭代后，都会导致任意相距很远的点（受吸引子的限制），在任何其他次数的迭代之后，都会导致任意接近的点。因此，具有混沌吸引子的动态系统是局部不稳定的但全局稳定的：一旦一些序列进入吸引子，附近的点就会彼此发散，但不会离开吸引子

如果吸引子具有[[分形]]结构，则称为“奇异”。当它的动力学是[[混沌理论|混沌]]时，通常会出现这种情况，但是[[奇异的非混沌吸引子]]也存在。如果一个<font color="#ff8000"> 奇异吸引子</font>是混沌的，表现出[[对初始条件的敏感依赖性]]，那么在吸引子上两个任意接近的备选初始点，经过任意多次迭代后，都会导致任意相距很远的点（受吸引子的限制），而在其他次数的迭代之后，都会导致任意接近的点。因此，具有混沌吸引子的动态系统是局部不稳定的但全局稳定的：一旦一些序列进入<font color="#ff8000"> 吸引子</font>，附近的点就会彼此发散，但不会离开<font color="#ff8000"> 吸引子</font>。

The term strange attractor was coined by David Ruelle and Floris Takens to describe the attractor resulting from a series of bifurcations of a system describing fluid flow. Strange attractors are often differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable. Strange attractors may also be found in the presence of noise, where they may be shown to support invariant random probability measures of Sinai–Ruelle–Bowen type.

The term strange attractor was coined by David Ruelle and Floris Takens to describe the attractor resulting from a series of bifurcations of a system describing fluid flow. Strange attractors are often differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable. Strange attractors may also be found in the presence of noise, where they may be shown to support invariant random probability measures of Sinai–Ruelle–Bowen type.

术语“奇异吸引子”是由[[David Ruelle]]和[[Floris Takens]]提出，用来描述一个描述流体流动的系统的一系列[[分岔理论|分叉]]所产生的吸引子。<ref>{{cite journal |last=Ruelle |first=David |last2=Takens |first2=Floris |date=1971 |title=On the nature of turbulence |url=http://projecteuclid.org/euclid.cmp/1103857186 |journal=Communications in Mathematical Physics |volume=20 |issue=3 |pages=167–192 |doi=10.1007/bf01646553}}</ref> 奇异吸引子通常在几个方向上[[可微函数|可微]]，但有些吸引子是[[同胚|样]]一个[[康托尘埃]]，因此不可微。在存在噪声的情况下，也可以发现奇异的吸引子，它们可以证明支持Sinai-Ruelle-Bowen型的不变随机概率测度。<ref name="Stochastic climate dynamics: Random attractors and time-dependent invariant measures">{{cite journal|author1=Chekroun M. D. |author2=Simonnet E. |author3=Ghil M. |author-link3=Michael Ghil |name-list-style=amp|

术语“奇异吸引子”是由[[David Ruelle]]和[[Floris Takens]]提出，用来描述一个描述流体流动的系统的一系列[[分岔理论|分叉]]所产生的吸引子。<ref>{{cite journal |last=Ruelle |first=David |last2=Takens |first2=Floris |date=1971 |title=On the nature of turbulence |url=http://projecteuclid.org/euclid.cmp/1103857186 |journal=Communications in Mathematical Physics |volume=20 |issue=3 |pages=167–192 |doi=10.1007/bf01646553}}</ref> 奇异吸引子通常在几个方向上[[可微函数|可微]]，但有些吸引子是[[同胚|类似]]的一个[[康托尘埃]]，因此不可微。在存在噪声的情况下，也可以发现奇异的吸引子，它们可以证明支持Sinai-Ruelle-Bowen型的不变随机概率测度。<ref name="Stochastic climate dynamics: Random attractors and time-dependent invariant measures">{{cite journal|author1=Chekroun M. D. |author2=Simonnet E. |author3=Ghil M. |author-link3=Michael Ghil |name-list-style=amp|

year = 2011 |

year = 2011 |

Examples of strange attractors include the [[Double scroll attractor|double-scroll attractor]], [[Hénon map|Hénon attractor]], [[Rössler attractor]], and [[Lorenz attractor]].

Examples of strange attractors include the [[Double scroll attractor|double-scroll attractor]], [[Hénon map|Hénon attractor]], [[Rössler attractor]], and [[Lorenz attractor]].

奇异吸引子的例子包括[[双滚动吸引子|双滚动吸引子]]、[[Hénon-map | Hénon吸引子]]、[[Rössler吸引子]]和[[Lorenz吸引子]]。

奇异吸引子的例子包括[[双涡旋吸引子|双涡旋吸引子]]、[[Hénon-map | Hénon吸引子]]、[[Rössler吸引子]]和[[Lorenz吸引子]]。

==Attractors characterize the evolution of a system吸引子表征系统的演化==

==Attractors characterize the evolution of a system吸引子表征系统的演化==