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In 1913, George David Birkhoff proved Poincaré's "Last Geometric Theorem", a special case of the three-body problem, a result that made him world-famous. In 1927, he published his [http://www.ams.org/online_bks/coll9/ Dynamical Systems]. Birkhoff's most durable result has been his 1931 discovery of what is now called the ergodic theorem. Combining insights from physics on the ergodic hypothesis with measure theory, this theorem solved, at least in principle, a fundamental problem of statistical mechanics. The ergodic theorem has also had repercussions for dynamics.
In 1913, George David Birkhoff proved Poincaré's "Last Geometric Theorem", a special case of the three-body problem, a result that made him world-famous. In 1927, he published his [http://www.ams.org/online_bks/coll9/ Dynamical Systems]. Birkhoff's most durable result has been his 1931 discovery of what is now called the ergodic theorem. Combining insights from physics on the ergodic hypothesis with measure theory, this theorem solved, at least in principle, a fundamental problem of statistical mechanics. The ergodic theorem has also had repercussions for dynamics.
1913年，乔治·戴维·伯克霍夫证明了庞加莱的“最后几何定理” ，这是三体的一个特例，这个结果使他闻名世界。1927年，他出版了《 http://www.ams.org/online_bks/coll9/动力系统》。伯克霍夫最持久的成果是他在1931年发现的遍历定理。这个定理结合了遍历假设物理学和测量理论的见解，至少在原则上解决了统计力学的一个基本问题。遍历定理也对动力学产生了影响。
1913年，乔治·戴维·伯克霍夫证明了庞加莱的“最后几何定理” ，这是三体的一个特例，这个结果使他闻名世界。1927年，他出版了《 [http://www.ams.org/online_bks/coll9/ 动力系统]》。伯克霍夫最持久的成果是他在1931年发现的遍历定理。这个定理结合了遍历假设物理学和测量理论的见解，至少在原则上解决了统计力学的一个基本问题。遍历定理也对动力学产生了影响。
在20世纪后期，巴勒斯坦机械工程师 Ali h. Nayfeh 将非线性动力学应用于机械和工程系统。他在应用非线性动力学方面的开创性工作对日常生活中常见的机器和结构的建造和维护产生了影响，如船舶、起重机、桥梁、建筑物、摩天大楼、喷气发动机、火箭发动机、飞机和航天器。
在20世纪后期，巴勒斯坦机械工程师 Ali h. Nayfeh 将非线性动力学应用于机械和工程系统。他在应用非线性动力学方面的开创性工作对日常生活中常见的机器和结构的建造和维护产生了影响，如船舶、起重机、桥梁、建筑物、摩天大楼、喷气发动机、火箭发动机、飞机和航天器。
==Basic definitions==
==Basic definitions==