NDLI: Computer-Assisted Proof of Shil'nikov Homoclinics: With Application to the Lorenz-84 Model

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Capiński, Maciej J. Wasieczko-Zajaͅc, Anna
Copyright Year	2017
Abstract	We present a methodology for computer-assisted proofs of Shil'nikov homoclinic intersections. It is based on geometric bounds on the invariant manifolds using rate conditions, and on propagating the bounds by an interval arithmetic integrator. Our method ensures uniqueness of the parameter for which the homoclinic takes place. We apply the method for the Lorenz-84 atmospheric circulation model, obtaining a sharp bound for the parameter, and also for where the homoclinic intersection of the stable/unstable manifolds takes place.
Sponsorship	Polish National Science Center
Starting Page	1453
Ending Page	1473
Page Count	21
File Format	PDF
DOI	10.1137/16M1079956
e-ISSN	15360040
Issue Number	3
Volume Number	16
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2017-08-03
Access Restriction	Subscribed
Subject Keyword	Homoclinic and heteroclinic solutions nontransversal intersections computer-assisted proofs invariant manifolds Hyperbolic orbits and sets Shil'nikov homoclinic Invariant manifold theory Algorithms with automatic result verification
Content Type	Text
Resource Type	Article

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