Under a Lie-algebra non-degeneracy condition, the top Lyapunov exponent of the slow-fast system (2.3) converges to E[λ(A(Z))] as the time-scale separation vanishes, implying ergodicity phase transitions in truncated fluid models.
Long exit times near a repelling equilibrium
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abstract
For a smooth vector field in a neighborhood of a critical point with all positive eigenvalues of the linearization, we consider the associated dynamics perturbed by white noise. Using Malliavin calculus tools, we obtain polynomial asymptotics for probabilities of atypically long exit times in the vanishing noise limit.
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Asymptotics of Lyapunov Exponents and Phase Transitions for Fluids with Degenerate Forcing
Under a Lie-algebra non-degeneracy condition, the top Lyapunov exponent of the slow-fast system (2.3) converges to E[λ(A(Z))] as the time-scale separation vanishes, implying ergodicity phase transitions in truncated fluid models.