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• W2373471818 abstract "The present work deals with numerical methods for computing slow stableinvariant manifolds as well as their invariant stable and unstable normalbundles. The slow manifolds studied here are sub-manifolds of the stablemanifold of a hyperbolic equilibrium point. Our approach is based on studyingcertain partial differential equations equations whose solutions parameterizethe invariant manifolds/bundles. Formal solutions of the partial differentialequations are obtained via power series arguments, and truncating the formalseries provides an explicit polynomial representation for the desired chartmaps. The coefficients of the formal series are given by recursion relationswhich are amenable to computer calculations. The parameterizations conjugatethe dynamics on the invariant manifolds and bundles to a prescribed lineardynamical systems. Hence in addition to providing accurate representation ofthe invariant manifolds and bundles our methods describe the dynamics on theseobjects as well. Example computations are given for vector fields which ariseas Galerkin projections of a partial differential equation. As an application weillustrate the use of the parameterized slow manifolds and their linear bundlesin the computation of heteroclinic orbits." @default.
• W2373471818 created "2016-06-24" @default.
• W2373471818 creator A5037325152 @default.
• W2373471818 creator A5088549920 @default.
• W2373471818 date "2016-05-01" @default.
• W2373471818 modified "2023-09-23" @default.
• W2373471818 title "Parameterization of slow-stable manifolds and their invariant vector bundles: Theory and numerical implementation" @default.
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• W2373471818 doi "https://doi.org/10.3934/dcds.2016002" @default.
• W2373471818 hasPublicationYear "2016" @default.
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