更改

<ref>{{Cite journal |title=The dynamical complexity of optically injected semiconductor lasers |first=S. |last=Wieczorek |first2=B. |last2=Krauskopf |first3=T. B. |last3=Simpson |lastauthoramp=yes |first4=D. |last4=Lenstra |journal=Physics Reports |volume=416 |issue=1–2 |year=2005 |pages=1–128 |doi=10.1016/j.physrep.2005.06.003 |bibcode = 2005PhR...416....1W }}</ref>以及一些理论上难以通过实验获得的例子中，如踢陀螺<ref>{{Cite journal |title=Quantum entanglement dependence on bifurcations and scars in non-autonomous systems. The case of quantum kicked top |first=G. |last=Stamatiou |lastauthoramp=yes |first2=D. P. K. |last2=Ghikas |journal=Physics Letters A |volume=368 |issue=3–4 |year=2007 |pages=206–214 |doi=10.1016/j.physleta.2007.04.003 |arxiv = quant-ph/0702172 |bibcode = 2007PhLA..368..206S }}</ref> 和耦合量子阱。<ref>{{Cite journal |title=Chaos in a Mean Field Model of Coupled Quantum Wells; Bifurcations of Periodic Orbits in a Symmetric Hamiltonian System |first=J. |last=Galan |first2=E. |last2=Freire |journal=Reports on Mathematical Physics |volume=44 |issue=1–2 |year=1999 |pages=87–94 |doi=10.1016/S0034-4877(99)80148-7 |bibcode=1999RpMP...44...87G}}</ref>正如[[Martin Gutzwiller]]在他关于量子混沌的经典著作中指出的那样，量子系统和经典运动方程之间存在联系的主要原因是在分岔时，经典轨道的特征变得很大。<ref>{{Cite journal |title=Beyond quantum mechanics: Insights from the work of Martin Gutzwiller |first=D. |last=Kleppner |first2=J. B. |last2=Delos |journal=Foundations of Physics |volume=31 |issue=4 |year=2001 |pages=593–612 |doi=10.1023/A:1017512925106 }}</ref><ref>{{Cite book |first=Martin C. |last=Gutzwiller |title=Chaos in Classical and Quantum Mechanics |year=1990 |publisher=Springer-Verlag |location=New York |isbn=978-0-387-97173-5 }}</ref>关于经典动力学和量子动力学之间的联系，人们研究了许多分岔，包括鞍结分岔、霍普夫分岔、脐点分岔、周期倍增分岔、重联分岔、切线分岔和尖点分岔。

<ref>{{Cite journal |title=The dynamical complexity of optically injected semiconductor lasers |first=S. |last=Wieczorek |first2=B. |last2=Krauskopf |first3=T. B. |last3=Simpson |lastauthoramp=yes |first4=D. |last4=Lenstra |journal=Physics Reports |volume=416 |issue=1–2 |year=2005 |pages=1–128 |doi=10.1016/j.physrep.2005.06.003 |bibcode = 2005PhR...416....1W }}</ref>以及一些理论上难以通过实验获得的例子中，如踢陀螺<ref>{{Cite journal |title=Quantum entanglement dependence on bifurcations and scars in non-autonomous systems. The case of quantum kicked top |first=G. |last=Stamatiou |lastauthoramp=yes |first2=D. P. K. |last2=Ghikas |journal=Physics Letters A |volume=368 |issue=3–4 |year=2007 |pages=206–214 |doi=10.1016/j.physleta.2007.04.003 |arxiv = quant-ph/0702172 |bibcode = 2007PhLA..368..206S }}</ref> 和耦合量子阱。<ref>{{Cite journal |title=Chaos in a Mean Field Model of Coupled Quantum Wells; Bifurcations of Periodic Orbits in a Symmetric Hamiltonian System |first=J. |last=Galan |first2=E. |last2=Freire |journal=Reports on Mathematical Physics |volume=44 |issue=1–2 |year=1999 |pages=87–94 |doi=10.1016/S0034-4877(99)80148-7 |bibcode=1999RpMP...44...87G}}</ref>正如[[Martin Gutzwiller]]在他关于量子混沌的经典著作中指出的那样，量子系统和经典运动方程之间存在联系的主要原因是在分岔时，经典轨道的特征变得很大。<ref>{{Cite journal |title=Beyond quantum mechanics: Insights from the work of Martin Gutzwiller |first=D. |last=Kleppner |first2=J. B. |last2=Delos |journal=Foundations of Physics |volume=31 |issue=4 |year=2001 |pages=593–612 |doi=10.1023/A:1017512925106 }}</ref><ref>{{Cite book |first=Martin C. |last=Gutzwiller |title=Chaos in Classical and Quantum Mechanics |year=1990 |publisher=Springer-Verlag |location=New York |isbn=978-0-387-97173-5 }}</ref>关于经典动力学和量子动力学之间的联系，人们研究了许多分岔，包括鞍结分岔、霍普夫分岔、脐点分岔、周期倍增分岔、重联分岔、切线分岔和尖点分岔。

==See also==

==另请参阅==

* [[Bifurcation diagram]]

* [[分叉记忆]]

* [[Bifurcation memory]]

* [[突变理论]]

* [[Catastrophe theory]]

* [[费根鲍姆常数]]

* [[Feigenbaum constants]]

* [[地磁反转]]

 

 

 

* [[Tennis racket theorem]]

==Notes==

==Notes==