| Abstract: |
| In nonlinear dynamics, basins of attraction link a given set of initial conditions to their corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology, and many other disciplines. Depending on the nature of the basins, prediction can be difficult even in systems that evolve under deterministic rules. To address this issue, we introduce the concept of basin entropy, a measure to quantify this uncertainty. Its application is illustrated with several paradigmatic examples that allow us to identify the ingredients that hinder the prediction of the final state. The basin entropy provides an efficient method to probe the behavior of a system when different parameters are varied. These ideas have been applied to some physical systems such as experiments of chaotic scattering of cold atoms, models of shadows of binary black holes, and classical and relativistic chaotic scattering associated to the H\`enon--Heiles Hamiltonian system in astrophysics. This is work in collaboration with Alvar Daza, Alexandre Wagemakers, Bertrand Georgeot, and David Gu\`ery-Odelin |
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