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→混沌系统的最小复杂度 Minimum complexity of a chaotic system
其中，<math>x</math>代表电场幅度 <math>G</math> <ref name="Okulov, A Yu 1986">{{cite journal |title=Space–temporal behavior of a light pulse propagating in a nonlinear nondispersive medium|journal=J. Opt. Soc. Am. B |volume=3 |issue=5 |pages=741–746 |year=1986 |last1= Okulov |first1=A Yu |last2=Oraevskiĭ |first2=A N |doi=10.1364/JOSAB.3.000741|bibcode=1986OSAJB...3..741O}}</ref>为激光增益分岔参数。<math>G</math>在区间<math>[0, \infty)</math>的逐渐增加使动力学从正规变成了混沌，<ref name="Okulov, A Yu 1986">{{cite journal |title=Space–temporal behavior of a light pulse propagating in a nonlinear nondispersive medium|journal=J. Opt. Soc. Am. B |volume=3 |issue=5 |pages=741–746 |year=1986 |last1= Okulov |first1=A Yu |last2=Oraevskiĭ |first2=A N |doi=10.1364/JOSAB.3.000741
其中，<math>x</math>代表电场幅度 <math>G</math> <ref name="Okulov, A Yu 1986">{{cite journal |title=Space–temporal behavior of a light pulse propagating in a nonlinear nondispersive medium|journal=J. Opt. Soc. Am. B |volume=3 |issue=5 |pages=741–746 |year=1986 |last1= Okulov |first1=A Yu |last2=Oraevskiĭ |first2=A N |doi=10.1364/JOSAB.3.000741|bibcode=1986OSAJB...3..741O}}</ref>为激光增益分岔参数。<math>G</math>在区间<math>[0, \infty)</math>的逐渐增加使动力学从正规变成了混沌，<ref name="Okulov, A Yu 1986">{{cite journal |title=Space–temporal behavior of a light pulse propagating in a nonlinear nondispersive medium|journal=J. Opt. Soc. Am. B |volume=3 |issue=5 |pages=741–746 |year=1986 |last1= Okulov |first1=A Yu |last2=Oraevskiĭ |first2=A N |doi=10.1364/JOSAB.3.000741
|bibcode=1986OSAJB...3..741O}}</ref> is laser gain as bifurcation parameter. The gradual increase of <math>G</math> at interval <math>[0, \infty)</math> changes dynamics from regular to chaotic one <ref name="Okulov, A Yu 1984">{{cite journal |doi=10.1070/QE1984v014n09ABEH006171
|bibcode=1986OSAJB...3..741O}}</ref><ref name="Okulov, A Yu 1984">{{cite journal |doi=10.1070/QE1984v014n09ABEH006171
|title=Regular and stochastic self-modulation in a ring laser with nonlinear element
|title=Regular and stochastic self-modulation in a ring laser with nonlinear element
|journal=Soviet Journal of Quantum Electronics |volume=14 |issue=2 |pages=1235–1237 |year=1984 |last1= Okulov |first1=A Yu |last2=Oraevskiĭ |first2=A N |bibcode=1984QuEle..14.1235O
|journal=Soviet Journal of Quantum Electronics |volume=14 |issue=2 |pages=1235–1237 |year=1984 |last1= Okulov |first1=A Yu |last2=Oraevskiĭ |first2=A N |bibcode=1984QuEle..14.1235O
虽然庞加莱-本迪克森定理表明欧氏平面上的连续动力系统不可能是混沌的，但具有非欧几里得几何的二维连续系统可以表现出混沌行为。<ref name="Rosario 2006">{{cite book|last=Rosario|first=Pedro|title=Underdetermination of Science: Part I|date=2006|publisher=Lulu.com|isbn=978-1411693913}}{{self-published source|date=February 2020}}</ref>也许令人惊讶的是，混沌也可能发生在线性系统中，只要它们是无限维的。.<ref>{{cite journal
虽然庞加莱-本迪克森定理表明欧氏平面上的连续动力系统不可能是混沌的，但具有非欧几里得几何的二维连续系统可以表现出混沌行为。<ref name="Rosario 2006">{{cite book|last=Rosario|first=Pedro|title=Underdetermination of Science: Part I|date=2006|publisher=Lulu.com|isbn=978-1411693913}}{{self-published source|date=February 2020}}</ref>也许令人惊讶的是，混沌也可能发生在线性系统中，只要它们是无限维的。<ref>{{cite journal
|last=Bonet |first=J. |last2=Martínez-Giménez |first2=F. |last3=Peris |first3=A.
|last=Bonet |first=J. |last2=Martínez-Giménez |first2=F. |last3=Peris |first3=A.
|year=2001
|year=2001
}}</ref> 线性混沌理论正在数学分析的一个分支——泛函分析中得到发展
}}</ref> 线性混沌理论正在数学分析的一个分支——泛函分析中得到发展
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===无限维地图 Infinite dimensional maps===
===无限维地图 Infinite dimensional maps===