Normal forms approach to diffusion near hyperbolic equilibria

Sergio Angel Almada Monter, Yuri Bakhtin

Research output: Contribution to journalArticlepeer-review


We consider the exit problem for small white noise perturbation of a smooth dynamical system on the plane in the neighbourhood of a hyperbolic critical point. We show that if the distribution of the initial condition has a scaling limit then the exit distribution and exit time also have a joint scaling limit as the noise intensity goes to zero. The limiting law is computed explicitly. The result completes the theory of noisy heteroclinic networks in two dimensions. The analysis is based on normal forms theory.

Original languageEnglish (US)
Pages (from-to)1883-1907
Number of pages25
Issue number6
StatePublished - Jun 2011

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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