Atypical exit events near a repelling equilibrium

@article{Bakhtin2019AtypicalEE,
  title={Atypical exit events near a repelling equilibrium},
  author={Yuri Bakhtin and Hong-Bin Chen},
  journal={arXiv: Probability},
  year={2019}
}
We consider exit problems for small white noise perturbations of a dynamical system generated by a vector field, and a domain containing a critical point with all positive eigenvalues of linearization. We prove that, in the vanishing noise limit, the probability of exit through a generic set on the boundary is asymptotically polynomial in the noise strength, with exponent depending on the mutual position of the set and the flag of the invariant manifolds associated with the top eigenvalues… 

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