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Moved page from wikipedia:en:Complex dynamics (history)
此词条暂由彩云小译翻译，翻译字数共251，未经人工整理和审校，带来阅读不便，请见谅。
{{Use American English|date = March 2019}}
{{Short description|Branch of mathematics}}
'''Complex dynamics''' is the study of [[dynamical system]]s defined by [[Iterated function|iteration]] of functions on [[complex number]] spaces. '''Complex analytic dynamics''' is the study of the dynamics of specifically [[analytic function]]s.
Complex dynamics is the study of dynamical systems defined by iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions.
复动力学是研究由复数空间上的函数迭代所定义的动力系统。复解析动力学是研究具体解析函数的动力学。
==Techniques==
==Techniques==
==Techniques==
*General<ref>''The Mandelbrot Set, Theme and Variations'' (London Mathematical Society Lecture Note Series) (No 274)
by [[Tan Lei]] (Editor), Cambridge University Press, 2000</ref>
**[[Montel's theorem]]
**[[Poincaré metric]]
**[[Schwarz lemma]]
**[[Riemann mapping theorem]]
**[[Carathéodory's theorem (conformal mapping)]]
**[[Böttcher's equation]]
*[[Combinatorics|Combinatorial]]<ref>{{Citation|url=http://comet.lehman.cuny.edu/keenl/FlekKeenJDEA.pdf|title=Boundaries of bounded Fatou components of quadratic maps|last1=Flek|first1=R|last2=Keen |first2=L|date=July 13, 2009|journal=Journal of Difference Equations and Applications|accessdate=2014-12-12}}</ref>
** Hubbard trees
** Spider algorithm<ref>{{cite journal|year=1991 |title=The Spider Algorithm|author=[[John H. Hubbard]] and Dierk Schleicher|url=http://www.math.cornell.edu/~hubbard/SpidersFinal.pdf}}</ref>
** Tuning
**[[Lamination (topology)|Laminations]]
**[[Cantor function|Devil's Staircase algorithm (Cantor function)]]
**[[Orbit portrait]]s
**[[Jean-Christophe Yoccoz|Yoccoz]] puzzles
*GeneralThe Mandelbrot Set, Theme and Variations (London Mathematical Society Lecture Note Series) (No 274)
by Tan Lei (Editor), Cambridge University Press, 2000
**Montel's theorem
**Poincaré metric
**Schwarz lemma
**Riemann mapping theorem
**Carathéodory's theorem (conformal mapping)
**Böttcher's equation
*Combinatorial
** Hubbard trees
** Spider algorithm
** Tuning
**Laminations
**Devil's Staircase algorithm (Cantor function)
**Orbit portraits
**Yoccoz puzzles
*
* 庞加莱定理
*
* 庞加莱定理
*
* 施瓦茨引理
*
* 黎曼映射定理
*
* Carathéodory 定理(保角映射)
*
* 伯特彻方程
*
* 组合式
*
* 哈伯德树
*
* 蜘蛛算法
*
* 调谐
*
* 层叠式
*
* 魔鬼楼梯算法(康托尔函数)
*
* 轨道人像
*
* 约科兹谜题
==Parts==
* '''Holomorphic dynamics''' (dynamics of [[holomorphic function]]s)<ref>[http://www.math.sunysb.edu/surveys-dynamical-systems Surveys in Dynamical systems available on-line at Dynamical Systems Homepage of Institute for Mathematical Sciences SUNY at Stony Brook]</ref>
** in one complex variable
** in several complex variables
* '''Conformal dynamics''' unites holomorphic dynamics in one complex variable with [[differentiable dynamics]] in one real variable.
* Holomorphic dynamics (dynamics of holomorphic functions)Surveys in Dynamical systems available on-line at Dynamical Systems Homepage of Institute for Mathematical Sciences SUNY at Stony Brook
** in one complex variable
** in several complex variables
* Conformal dynamics unites holomorphic dynamics in one complex variable with differentiable dynamics in one real variable.
全纯动力学(全纯函数的动力学)动力学系统的调查可在动力学系统在线获得。斯托尼布鲁克州立大学数学科学研究所首页
*
* 在一个复杂的变量中
*
* 在几个复杂的变量中
* 共形动力学将全纯动力学在一个复杂的变量中与一个实变量中的可微动力学结合起来。
== See also ==
*[[Arithmetic dynamics]]
*[[Chaos theory]]
*[[Complex analysis]]
*[[Complex quadratic polynomial]]
*[[Fatou set]]
*[[Infinite compositions of analytic functions]]
*[[Julia set]]
*[[Mandelbrot set]]
*[[Symbolic dynamics]]
*Arithmetic dynamics
*Chaos theory
*Complex analysis
*Complex quadratic polynomial
*Fatou set
*Infinite compositions of analytic functions
*Julia set
*Mandelbrot set
*Symbolic dynamics
= = 参见同样 = =
* 算术动态系统
* 混沌理论
* 复杂分析
* 复杂二次多项式
* Fatou 集
* 解析函数的无穷组合
* Julia 集
* Mandelbrot 集
* 符号动力学
==Notes==
{{reflist}}
==References==
*Alan F. Beardon, ''[https://books.google.com/books?id=u3_FBg7nFHAC Iteration of Rational Functions: complex analytic dynamical systems]'', Springer, 2000, {{ISBN|978-0-387-95151-5}}
*Araceli Bonifant, Misha Lyubich, Scott Sutherland (editors), ''[http://press.princeton.edu/titles/10167.html Frontiers in Complex Dynamics]'', [[Princeton University Press]], 2014.
*Daniel S. Alexander, ''[https://link.springer.com/book/10.1007/978-3-663-09197-4 A History of Complex Dynamics: From Schröder to Fatou and Julia]'', Aspect of Mathematics, 1994, {{ISBN|978-3-663-09199-8}}
*[[Lennart Carleson]], Theodore W. Gamelin, ''[https://books.google.com/books?id=M-I8qRE8HGUC Complex Dynamics]'', Springer, 1993, {{ISBN|978-0-387-97942-7}}
*[[John Milnor]], ''[https://books.google.co.uk/books?id=DsthOelUMlkC&printsec=frontcover Dynamics in One Complex Variable]'' (Third edition), [[Princeton University Press]], 2006
*Shunsuke Morosawa, Y. Nishimura, M. Taniguchi, T. Ueda, ''[https://books.google.com/books?id=9wb4S_ES4h4C Holomorphic Dynamics]'', Cambridge University Press, 2000, {{ISBN|978-0-521-66258-1}}
*Alan F. Beardon, Iteration of Rational Functions: complex analytic dynamical systems, Springer, 2000,
*Araceli Bonifant, Misha Lyubich, Scott Sutherland (editors), Frontiers in Complex Dynamics, Princeton University Press, 2014.
*Daniel S. Alexander, A History of Complex Dynamics: From Schröder to Fatou and Julia, Aspect of Mathematics, 1994,
*Lennart Carleson, Theodore W. Gamelin, Complex Dynamics, Springer, 1993,
*John Milnor, Dynamics in One Complex Variable (Third edition), Princeton University Press, 2006
*Shunsuke Morosawa, Y. Nishimura, M. Taniguchi, T. Ueda, Holomorphic Dynamics, Cambridge University Press, 2000,
= = References = =
* 艾伦 · F · 比尔登，《理性函数的迭代: 复杂分析动力系统》 ，斯普林格出版社，2000年，
* 阿拉塞利 · 博尼凡特，米沙 · 柳比奇，斯科特 · 萨瑟兰(编辑) ，《复动力学的前沿》 ，普林斯顿大学出版社出版社，2014年。
* 丹尼尔 · S · 亚历山大，《复动力学的历史: 从施罗德到法图和茱莉亚，数学的方面，1994》 ，
* 里纳特·卡尔松，西奥多 · W · 甘末林，复动力学，斯普林格，1993，
* 约翰 · 米尔诺，《一个复变量中的动力学》(第三版) ，普林斯顿大学出版社，2006
* 森泽俊介，西村，M · 谷口，上田，全形动力学，剑桥大学出版社，2000,
[[Category:Complex dynamics| ]]
[[Category:Emergence]]
Category:Emergence
分类: 涌现
{{mathanalysis-stub}}
<noinclude>
<small>This page was moved from [[wikipedia:en:Complex dynamics]]. Its edit history can be viewed at [[复杂动力系统/edithistory]]</small></noinclude>
[[Category:待整理页面]]
{{Use American English|date = March 2019}}
{{Short description|Branch of mathematics}}
'''Complex dynamics''' is the study of [[dynamical system]]s defined by [[Iterated function|iteration]] of functions on [[complex number]] spaces. '''Complex analytic dynamics''' is the study of the dynamics of specifically [[analytic function]]s.
Complex dynamics is the study of dynamical systems defined by iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions.
复动力学是研究由复数空间上的函数迭代所定义的动力系统。复解析动力学是研究具体解析函数的动力学。
==Techniques==
==Techniques==
==Techniques==
*General<ref>''The Mandelbrot Set, Theme and Variations'' (London Mathematical Society Lecture Note Series) (No 274)
by [[Tan Lei]] (Editor), Cambridge University Press, 2000</ref>
**[[Montel's theorem]]
**[[Poincaré metric]]
**[[Schwarz lemma]]
**[[Riemann mapping theorem]]
**[[Carathéodory's theorem (conformal mapping)]]
**[[Böttcher's equation]]
*[[Combinatorics|Combinatorial]]<ref>{{Citation|url=http://comet.lehman.cuny.edu/keenl/FlekKeenJDEA.pdf|title=Boundaries of bounded Fatou components of quadratic maps|last1=Flek|first1=R|last2=Keen |first2=L|date=July 13, 2009|journal=Journal of Difference Equations and Applications|accessdate=2014-12-12}}</ref>
** Hubbard trees
** Spider algorithm<ref>{{cite journal|year=1991 |title=The Spider Algorithm|author=[[John H. Hubbard]] and Dierk Schleicher|url=http://www.math.cornell.edu/~hubbard/SpidersFinal.pdf}}</ref>
** Tuning
**[[Lamination (topology)|Laminations]]
**[[Cantor function|Devil's Staircase algorithm (Cantor function)]]
**[[Orbit portrait]]s
**[[Jean-Christophe Yoccoz|Yoccoz]] puzzles
*GeneralThe Mandelbrot Set, Theme and Variations (London Mathematical Society Lecture Note Series) (No 274)
by Tan Lei (Editor), Cambridge University Press, 2000
**Montel's theorem
**Poincaré metric
**Schwarz lemma
**Riemann mapping theorem
**Carathéodory's theorem (conformal mapping)
**Böttcher's equation
*Combinatorial
** Hubbard trees
** Spider algorithm
** Tuning
**Laminations
**Devil's Staircase algorithm (Cantor function)
**Orbit portraits
**Yoccoz puzzles
*
* 庞加莱定理
*
* 庞加莱定理
*
* 施瓦茨引理
*
* 黎曼映射定理
*
* Carathéodory 定理(保角映射)
*
* 伯特彻方程
*
* 组合式
*
* 哈伯德树
*
* 蜘蛛算法
*
* 调谐
*
* 层叠式
*
* 魔鬼楼梯算法(康托尔函数)
*
* 轨道人像
*
* 约科兹谜题
==Parts==
* '''Holomorphic dynamics''' (dynamics of [[holomorphic function]]s)<ref>[http://www.math.sunysb.edu/surveys-dynamical-systems Surveys in Dynamical systems available on-line at Dynamical Systems Homepage of Institute for Mathematical Sciences SUNY at Stony Brook]</ref>
** in one complex variable
** in several complex variables
* '''Conformal dynamics''' unites holomorphic dynamics in one complex variable with [[differentiable dynamics]] in one real variable.
* Holomorphic dynamics (dynamics of holomorphic functions)Surveys in Dynamical systems available on-line at Dynamical Systems Homepage of Institute for Mathematical Sciences SUNY at Stony Brook
** in one complex variable
** in several complex variables
* Conformal dynamics unites holomorphic dynamics in one complex variable with differentiable dynamics in one real variable.
全纯动力学(全纯函数的动力学)动力学系统的调查可在动力学系统在线获得。斯托尼布鲁克州立大学数学科学研究所首页
*
* 在一个复杂的变量中
*
* 在几个复杂的变量中
* 共形动力学将全纯动力学在一个复杂的变量中与一个实变量中的可微动力学结合起来。
== See also ==
*[[Arithmetic dynamics]]
*[[Chaos theory]]
*[[Complex analysis]]
*[[Complex quadratic polynomial]]
*[[Fatou set]]
*[[Infinite compositions of analytic functions]]
*[[Julia set]]
*[[Mandelbrot set]]
*[[Symbolic dynamics]]
*Arithmetic dynamics
*Chaos theory
*Complex analysis
*Complex quadratic polynomial
*Fatou set
*Infinite compositions of analytic functions
*Julia set
*Mandelbrot set
*Symbolic dynamics
= = 参见同样 = =
* 算术动态系统
* 混沌理论
* 复杂分析
* 复杂二次多项式
* Fatou 集
* 解析函数的无穷组合
* Julia 集
* Mandelbrot 集
* 符号动力学
==Notes==
{{reflist}}
==References==
*Alan F. Beardon, ''[https://books.google.com/books?id=u3_FBg7nFHAC Iteration of Rational Functions: complex analytic dynamical systems]'', Springer, 2000, {{ISBN|978-0-387-95151-5}}
*Araceli Bonifant, Misha Lyubich, Scott Sutherland (editors), ''[http://press.princeton.edu/titles/10167.html Frontiers in Complex Dynamics]'', [[Princeton University Press]], 2014.
*Daniel S. Alexander, ''[https://link.springer.com/book/10.1007/978-3-663-09197-4 A History of Complex Dynamics: From Schröder to Fatou and Julia]'', Aspect of Mathematics, 1994, {{ISBN|978-3-663-09199-8}}
*[[Lennart Carleson]], Theodore W. Gamelin, ''[https://books.google.com/books?id=M-I8qRE8HGUC Complex Dynamics]'', Springer, 1993, {{ISBN|978-0-387-97942-7}}
*[[John Milnor]], ''[https://books.google.co.uk/books?id=DsthOelUMlkC&printsec=frontcover Dynamics in One Complex Variable]'' (Third edition), [[Princeton University Press]], 2006
*Shunsuke Morosawa, Y. Nishimura, M. Taniguchi, T. Ueda, ''[https://books.google.com/books?id=9wb4S_ES4h4C Holomorphic Dynamics]'', Cambridge University Press, 2000, {{ISBN|978-0-521-66258-1}}
*Alan F. Beardon, Iteration of Rational Functions: complex analytic dynamical systems, Springer, 2000,
*Araceli Bonifant, Misha Lyubich, Scott Sutherland (editors), Frontiers in Complex Dynamics, Princeton University Press, 2014.
*Daniel S. Alexander, A History of Complex Dynamics: From Schröder to Fatou and Julia, Aspect of Mathematics, 1994,
*Lennart Carleson, Theodore W. Gamelin, Complex Dynamics, Springer, 1993,
*John Milnor, Dynamics in One Complex Variable (Third edition), Princeton University Press, 2006
*Shunsuke Morosawa, Y. Nishimura, M. Taniguchi, T. Ueda, Holomorphic Dynamics, Cambridge University Press, 2000,
= = References = =
* 艾伦 · F · 比尔登，《理性函数的迭代: 复杂分析动力系统》 ，斯普林格出版社，2000年，
* 阿拉塞利 · 博尼凡特，米沙 · 柳比奇，斯科特 · 萨瑟兰(编辑) ，《复动力学的前沿》 ，普林斯顿大学出版社出版社，2014年。
* 丹尼尔 · S · 亚历山大，《复动力学的历史: 从施罗德到法图和茱莉亚，数学的方面，1994》 ，
* 里纳特·卡尔松，西奥多 · W · 甘末林，复动力学，斯普林格，1993，
* 约翰 · 米尔诺，《一个复变量中的动力学》(第三版) ，普林斯顿大学出版社，2006
* 森泽俊介，西村，M · 谷口，上田，全形动力学，剑桥大学出版社，2000,
[[Category:Complex dynamics| ]]
[[Category:Emergence]]
Category:Emergence
分类: 涌现
{{mathanalysis-stub}}
<noinclude>
<small>This page was moved from [[wikipedia:en:Complex dynamics]]. Its edit history can be viewed at [[复杂动力系统/edithistory]]</small></noinclude>
[[Category:待整理页面]]