佩雷尔曼博士利用广为人知的“瑞奇流（Ricci flow）”这样一个热方程来证明了庞加莱猜想。

Dr Perelman proved Poincaré's conjecture by taking an equation normally used to model heat dissipation in three-dimensional objects, known as Ricci flow.

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方法利用庞加莱截面、李雅普·诺夫指数、关联维等工具分别对抛物方程和椭圆方程的非线性动力学行为进行描述。

Methods Nonlinear dynamical behavior of both parabolic equation and elliptic equation were investigated by several tools such as Poincare section, Lyapunov exponent, and correlation dimension.

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