On the probability of finding a nonphysical solution through shadowing

DOI10.1016/J.JCP.2021.110389arXiv2010.13768MaRDI QIDQ6352279

Publication date: 26 October 2020

Abstract: This paper proves that shadowing solutions can be almost surely nonphysical. This finding invalidates the argument that small perturbations in a chaotic system can only have a small impact on its statistical behavior. This theoretical finding has implications for many applications in which chaotic mechanics plays an important role. It suggests, for example, that we can control the climate through subtle perturbations. It also suggests that numerical simulations of chaotic dynamics, such as turbulent flows, may fail to predict the true long-term or statistical behavior.

Mathematics Subject Classification ID

Ergodic theory (37Axx) Smooth dynamical systems: general theory (37Cxx) Dynamical systems with hyperbolic behavior (37Dxx)

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