证明了一类非线性离散动力系统不动点的两个判别方法，具体分析了两个不同类型的离散动力系统的不动点性质及其分岔特性。

Some nonlinear discrete dynamic systems are considered, and two discriminating methods of the fixed point are proved. The bifurcation behavior of the corresponding dynamic systems is also studied.

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这幅图片展示了曼德尔勃特集合(Mandelbrot set)与离散混沌动力系统(logistic map)之间的一致性，这解释了复杂而无序的行为可以由简单的非线性动态方程序中得出。

This graph shows correspondence between the Mandelbrot set and the logistic map, which explains how complex, chaotic behavior can arise from simple non-linear dynamical equations.

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