更改

<center> 三体问题的混乱运动(计算机模拟) </center>

<center> 三体问题的混乱运动(计算机模拟) </center>

====Assessments on Poincaré and relativity====

====Assessments on Poincaré and relativity对庞加莱和相对论的评价====

Poincaré published two now classical monographs, "New Methods of Celestial Mechanics" (1892–1899) and "Lectures on Celestial Mechanics" (1905–1910). In them, he successfully applied the results of their research to the problem of the motion of three bodies and studied in detail the behavior of solutions (frequency, stability, asymptotic, and so on). They introduced the small parameter method, fixed points, integral invariants, variational equations, the convergence of the asymptotic expansions. Generalizing a theory of Bruns (1887), Poincaré showed that the three-body problem is not integrable. In other words, the general solution of the three-body problem can not be expressed in terms of algebraic and transcendental functions through unambiguous coordinates and velocities of the bodies. His work in this area was the first major achievement in celestial mechanics since Isaac Newton.

Poincaré published two now classical monographs, "New Methods of Celestial Mechanics" (1892–1899) and "Lectures on Celestial Mechanics" (1905–1910). In them, he successfully applied the results of their research to the problem of the motion of three bodies and studied in detail the behavior of solutions (frequency, stability, asymptotic, and so on). They introduced the small parameter method, fixed points, integral invariants, variational equations, the convergence of the asymptotic expansions. Generalizing a theory of Bruns (1887), Poincaré showed that the three-body problem is not integrable. In other words, the general solution of the three-body problem can not be expressed in terms of algebraic and transcendental functions through unambiguous coordinates and velocities of the bodies. His work in this area was the first major achievement in celestial mechanics since Isaac Newton.

庞加莱出版了两本经典专著《天体力学》(1892-1899)和《天体力学》(1905-1910)。其中，他成功地将他们的研究成果应用于三体运动问题，并详细研究了解的行为(频率、稳定性、渐近性等)。介绍了小参数方法、不动点、积分不变量、变分方程、渐近展开式的收敛性。将 Bruns (1887)的理论进行概括，poincaré 指出三体不可积。换句话说，三体的一般解不能通过物体的明确坐标和速度用代数函数和超越函数来表示。他在这个领域的工作是自艾萨克 · 牛顿以来天体力学的第一个重大成就。

庞加莱出版了两本经典专著《天体力学》(1892-1899)和《天体力学》(1905-1910)。其中，他成功地将他们的研究成果应用于三体运动问题，并详细研究了解的行为(频率、稳定性、渐近性等)。介绍了小参数方法、不动点、积分不变量、变分方程、渐近展开式的收敛性。将 布鲁斯Bruns (1887)的理论进行概括，庞加莱 指出三体不可积。换句话说，三体的一般解不能通过物体的明确坐标和速度用代数函数和超越函数来表示。他在这个领域的工作是自艾萨克 · 牛顿以来天体力学的第一个重大成就。

{{Further|History of special relativity|Relativity priority dispute}}

{{Further|History of special relativity|Relativity priority dispute}}

Poincaré's work in the development of special relativity is well recognised,<ref name=darrigol /> though most historians stress that despite many similarities with Einstein's work, the two had very different research agendas and interpretations of the work.<ref>Galison 2003 and Kragh 1999, Secondary sources on relativity</ref> Poincaré developed a similar physical interpretation of local time and noticed the connection to signal velocity, but contrary to Einstein he continued to use the ether-concept in his papers and argued that clocks at rest in the ether show the "true" time, and moving clocks show the local time. So Poincaré tried to keep the relativity principle in accordance with classical concepts, while Einstein developed a mathematically equivalent kinematics based on the new physical concepts of the relativity of space and time.<ref>Holton (1988), 196–206</ref><ref>Hentschel (1990), 3–13{{full citation needed|date=September 2019}}</ref><ref>Miller (1981), 216–217</ref><ref>Darrigol (2005), 15–18</ref><ref>Katzir (2005), 286–288</ref>

Poincaré's work in the development of special relativity is well recognised,<ref name=darrigol /> though most historians stress that despite many similarities with Einstein's work, the two had very different research agendas and interpretations of the work.<ref>Galison 2003 and Kragh 1999, Secondary sources on relativity</ref> Poincaré developed a similar physical interpretation of local time and noticed the connection to signal velocity, but contrary to Einstein he continued to use the ether-concept in his papers and argued that clocks at rest in the ether show the "true" time, and moving clocks show the local time. So Poincaré tried to keep the relativity principle in accordance with classical concepts, while Einstein developed a mathematically equivalent kinematics based on the new physical concepts of the relativity of space and time.<ref>Holton (1988), 196–206</ref><ref>Hentschel (1990), 3–13{{full citation needed|date=September 2019}}</ref><ref>Miller (1981), 216–217</ref><ref>Darrigol (2005), 15–18</ref><ref>Katzir (2005), 286–288</ref>

These monographs include an idea of Poincaré, which later became the basis for mathematical "chaos theory" (see, in particular, the Poincaré recurrence theorem) and the general theory of dynamical systems.

These monographs include an idea of Poincaré, which later became the basis for mathematical "chaos theory" (see, in particular, the Poincaré recurrence theorem) and the general theory of dynamical systems.

While this is the view of most historians, a minority go much further, such as [[E. T. Whittaker]], who held that Poincaré and Lorentz were the true discoverers of relativity.<ref>Whittaker 1953, Secondary sources on relativity</ref>

While this is the view of most historians, a minority go much further, such as [[E. T. Whittaker]], who held that Poincaré and Lorentz were the true discoverers of relativity.<ref>Whittaker 1953, Secondary sources on relativity</ref>

===Algebra and number theory===

===Algebra and number theory===