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

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