Chapitre D'ouvrage Année : 2025

Will We Continue to Use Chaotic Attractors in Science for a Long Time, or Will They only Be a Passing Curiosity?

Résumé

Since the founding work of Henri Poincar´e in 1889 on the three-body problem, and the paradigm shift in the study of nonlinear dynamical system and the turbulence model occurred in 1970 with the work of Ruelle and Takens who introduced the concept of strange chaotic attractor, numerous applications have emerged in different domains (economics, electronics, cryptography, physics, etc.). We try to describe the evolution of these objects over the last half century and to find out what their place is not only in mathematics, but also for the progress of science, and whether they will be used long into the future.

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Dates et versions

hal-05011216 , version 1 (29-03-2025)

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René Lozi. Will We Continue to Use Chaotic Attractors in Science for a Long Time, or Will They only Be a Passing Curiosity?. New Developments in Discrete Dynamical Systems, Difference Equations, and Applications. ICDEA 2023, Springer Proceedings in Mathematics & Statistics, 485, Springer Nature Switzerland, pp.203-232, 2025, Springer Proceedings in Mathematics & Statistics, 978-3-031-82002-1. ⟨10.1007/978-3-031-82003-8_10⟩. ⟨hal-05011216⟩
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