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dc.contributor.authorVan Den Berg, J.B.
dc.contributor.authorMireles-James, J.D.
dc.contributor.authorLessard, J.-P.
dc.contributor.authorMischaikow, K.
dc.description.abstractIn this paper we propose a rigorous numerical technique for the computation of symmetric connecting orbits for ordinary differential equations. The idea is to solve a projected boundary value problem (BVP) in a function space via a fixed point argument. The formulation of the projected BVP involves a high order parameterization of the invariant manifolds at the steady states. Using this parameterization, one can obtain explicit exponential asymptotic bounds for the coefficients of the expansion of the manifolds. Combining these bounds with piecewise linear approximations, one can construct a contraction in a function space whose unique fixed point corresponds to the wanted connecting orbit. We have implemented the method to demonstrate its effectiveness, and we have used it to prove the existence of a family of even homoclinic orbits for the Gray-Scott equation.
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectComputer assisted proof
dc.subjectInvariant manifolds
dc.subjectParameterization method
dc.subjectProjected boundary conditions
dc.subjectRadii polynomials
dc.subjectValidated continuation
dc.titleRigorous numerics for symmetric connecting orbits: Even homoclinics of the Gray-Scott equationen_US
dc.journal.titleSIAM Journal on Mathematical Analysisen_US

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Reconocimiento-NoComercial-CompartirIgual 3.0 España
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