Summary
We consider diffusion random perturbations of a dynamical systemS t in a domainG⊂R m which, in particular, may be invariant under the action ofS t. Continuing the study of [K1-K4] we find the asymptotic behavior of the principal eigenvalue of the corresponding generator when the diffusion term tends to zero.
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This work was supported by U.S.A.-Israel B.S.F. Grant #84-00028
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Eizenberg, A., Kifer, Y. The asymptotic behavior of the principal eigenvalue in a singular perturbation problem with invariant boundaries. Probab. Th. Rel. Fields 76, 439–476 (1987). https://doi.org/10.1007/BF00960068
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DOI: https://doi.org/10.1007/BF00960068