查看“︁厄农映射”︁的源代码

[[Image:HenonMap.svg|thumb|''a'' = 1.4、''b'' = 0.3时的厄农吸引子]] 
'''厄农映射'''（{{lang-en|Hénon map}}）是一种可以产生[[混沌]]现象的离散时间[[动态系统]]，其迭代表达式为：
:<math>\begin{cases}x_{n+1} = 1-a x_n^2 + y_n\\y_{n+1} = b x_n.\end{cases}</math>
在'''经典厄农映射'''中，参数值分别取为''a''&nbsp;=&nbsp;1.4及''b''&nbsp;=&nbsp;0.3。此时，系统表现出混沌现象。而当''a''与''b''取其他不同值时，系统可表现为混沌现象、阵发性现象，或收敛至[[周期点]]。通过轨道图可以看出不同参数下系统的行为特征。

厄农映射是由法国数学家{{le|米歇尔·厄农|Michel Hénon}}提出的，以此作为[[洛伦茨吸引子|洛伦茨模型]]的[[庞加莱截面]]的简化模型。对经典厄农映射而言，任意初始点或趋向厄农[[奇异吸引子]]，或发散至无穷大。厄农吸引子具有[[分形]]结构，其在一个方向上连续，另一个方向上则为一个[[康托尔集]]。数值计算表明经典厄农吸引子的[[关联维数]]为1.25&nbsp;±&nbsp;0.02<ref name="Grassberger 1983">{{cite journal |author1=P. Grassberger |author2=I. Procaccia | title=Measuring the strangeness of strange attractors | journal=Physica | year=1983 | volume=9D | issue=1-2| pages=189–208| bibcode=1983PhyD....9..189G | doi=10.1016/0167-2789(83)90298-1  }}</ref>，[[豪斯多夫维数]]为1.261&nbsp;±&nbsp;0.003。<ref name="Russell 1980">{{cite journal |author1=D.A. Russell |author2=J.D. Hanson |author3=E. Ott | title=Dimension of strange attractors | journal=Physical Review Letters | year=1980 | volume=45 | issue=14 | pages=1175| doi= 10.1103/PhysRevLett.45.1175 | bibcode=1980PhRvL..45.1175R}}</ref>

== 参考文献 ==
{{reflist}}
* {{cite journal | author=M. Hénon | title=A two-dimensional mapping with a strange attractor | url=https://archive.org/details/sim_communications-in-mathematical-physics_1976_50_1/page/69 | journal=Communications in Mathematical Physics | year=1976 | volume=50 | issue=1 | pages=69–77 | doi=10.1007/BF01608556|bibcode = 1976CMaPh..50...69H }}
* {{cite journal
|journal = Physical Review A 
|year = 1988
|title = Topological and metric properties of Hénon-type strange attractors
|pages = 1503–1520
|issue = 3
|author1=Predrag Cvitanović |author2=Gemunu Gunaratne |author3=Itamar Procaccia |volume = 38
|doi = 10.1103/PhysRevA.38.1503
|pmid=9900529
|bibcode = 1988PhRvA..38.1503C }}
* {{cite journal | author1=M. Michelitsch | author2=O. E. Rössler | title=A New Feature in Hénon's Map | journal=Computers & Graphics | year=1989 | volume=13 | issue=2 | pages=263–265 | url=http://mathworld.wolfram.com/HenonMap.html | doi=10.1016/0097-8493(89)90070-8 | access-date=2016-12-03 | archive-date=2021-01-25 | archive-url=https://web.archive.org/web/20210125021139/https://mathworld.wolfram.com/HenonMap.html | dead-url=no }}. Reprinted in: Chaos and Fractals, A Computer Graphical Journey: Ten Year Compilation of Advanced Research (Ed. C. A. Pickover). Amsterdam, Netherlands: Elsevier, pp.&nbsp;69–71, 1998

{{混沌理论}}

[[Category:混沌映射]]