2020/12/13 by Miguel A. F. Sanjuán, Sanjuan, Miguel A. F.
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Complex Systems and Time Series Analysis #Computational Physics and Python Applications #FOS: Physical sciences #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2012.07115
openalex publication_date 2020/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.