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We present a methodology for computer assisted proofs of Shil'nikovhomoclinic intersections. It is based on geometric bounds on the invariantmanifolds using rate conditions, and on propagating the bounds by an intervalarithmetic integrator. Our method ensures uniqueness of the parameter for whichthe homoclinic takes place. We apply the method for the Lorenz-84 atmosphericcirculation model, obtaining a sharp bound for the parameter, and also forwhere the homoclinic intersection of the stable/unstable manifolds takes place.

Computer assisted proof of Shil'nikov homoclinics: with application to the Lorenz-84 model