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Journal Articles Proceedings of the Royal Society of London A Mathematical and Physical Sciences Year : 2022

Non-hyperbolicity at large scales of a high-dimensional chaotic system

Abstract

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 discretisation. 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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Dates and versions

hal-03675948 , version 1 (23-05-2022)

Identifiers

  • HAL Id : hal-03675948 , version 1

Cite

Caroline Wormell. Non-hyperbolicity at large scales of a high-dimensional chaotic system. Proceedings of the Royal Society of London A Mathematical and Physical Sciences, 2022, 478, pp.2261. ⟨hal-03675948⟩
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