On the probability of finding a nonphysical solution through shadowing
arXiv:2010.13768 · doi:10.1016/j.jcp.2021.110389
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.
arXiv comment33 pages
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- Risk-averse design of tall buildings for uncertain wind conditions
- A Self-Adaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos
- Space-split algorithm for sensitivity analysis of discrete chaotic systems with unstable manifolds of arbitrary dimension