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arXiv · 2012.07115

Unpredictability, Uncertainty and Fractal Structures in Physics

Miguel A. F. Sanjuan
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Abstract

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.

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Miguel A. F. Sanjuan. 2020-12-13. Unpredictability, Uncertainty and Fractal Structures in Physics. https://arxiv.org/abs/2012.07115

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