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Since the founding work of Henri Poincaré 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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Will We Continue to Use Chaotic Attractors in Science for a Long Time, or Will They only Be a Passing Curiosity?

  • 会议论文

  • 发表日期：

    2025年

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  • René Lozi

摘要

Since the founding work of Henri Poincaré 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.