论文标题
物理学中的不可预测性，不确定性和分形结构
Unpredictability, Uncertainty and Fractal Structures in Physics
论文作者
论文摘要
在物理学中，我们有法律决定给定物理系统的时间演变，具体取决于其参数及其初始条件。当我们拥有多稳定系统时，许多吸引子共存，因此它们的吸引盆地可能具有分形甚至WADA边界，以使预测变得更加复杂，具体取决于初始条件。混沌系统通常在相空间中呈现分形盆地。在初始条件下的微小不确定性导致最终状态行为的某种不可预测性。盆地熵的新概念提供了一种新的定量方法，以测量吸引盆地中最终状态的不可预测性。混乱理论的简单方法可以更好地理解物理学和其他科学学科的基本问题。
In Physics, we have laws that determine the time evolution of a given physical system, depending on its parameters and its initial conditions. When we have multi-stable systems, many attractors coexist so that their basins of attraction might possess fractal or even Wada boundaries in such a way that the prediction becomes more complicated depending on the initial conditions. Chaotic systems typically present fractal basins in phase space. A small uncertainty in the initial conditions gives rise to a certain unpredictability of the final state behavior. The new notion of basin entropy provides a new quantitative way to measure the unpredictability of the final states in basins of attraction. Simple methods from chaos theory can contribute to a better understanding of fundamental questions in physics as well as other scientific disciplines.
