期刊
出版社
ROYAL SOC
DOI: 10.1098/rspa.2021.0808
关键词
chaotic hypothesis; coupled maps; wild dynamics; non-hyperbolic systems; thermodynamic limit
The dynamics of many important high-dimensional dynamical systems are chaotic and complex. The widely accepted chaotic hypothesis by Gallavotti and Cohen is challenged by our numerical evidence which shows the existence of non-hyperbolic large-scale dynamical structures in a mean-field coupled system. This suggests that the chaotic hypothesis should not be assumed to hold in all systems, and a better understanding of its validity is required.
The dynamics of many important high-dimensional dynamical systems are both chaotic and complex, meaning that strong reducing hypotheses are required to understand the dynamics. The highly influential chaotic hypothesis of Gallavotti and Cohen states that the large-scale dynamics of high-dimensional systems are effectively uniformly hyperbolic, which implies many felicitous statistical properties. We obtain direct and reliable numerical evidence, contrary to the chaotic hypothesis, of the existence of non-hyperbolic large-scale dynamical structures in a mean-field coupled system. To do this, we reduce the system to its thermodynamic limit, which we approximate numerically with a Chebyshev basis transfer operator discretization. This enables us to obtain a high-precision estimate of a homoclinic tangency, implying a failure of uniform hyperbolicity. Robust non-hyperbolic behaviour is expected under perturbation. As a result, the chaotic hypothesis should not be a priori assumed to hold in all systems, and a better understanding of the domain of its validity is required.
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