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- W2029226578 abstract "We describe an efficient and accurate numerical method for computing smooth approximations to invariant manifolds of planar maps, based on geometric modeling ideas from Computer Aided Geometric Design (CAGD). The unstable manifold of a hyperbolic fixed point is modeled by a piecewise Bézier interpolant (a Catmull–Rom spline) and properties of such curves are used to define a rule for adaptively adding points to ensure that the approximation resolves the manifold to within a specified tolerance. Numerical tests on a variety of example mappings demonstrate that the new method produces a manifold of a given accuracy with far fewer calls to the map, compared with previous methods. A brief introduction to the relevant ideas from CAGD is provided." @default.
- W2029226578 created "2016-06-24" @default.
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- W2029226578 date "2011-07-01" @default.
- W2029226578 modified "2023-10-14" @default.
- W2029226578 title "HIGH-ORDER BISECTION METHOD FOR COMPUTING INVARIANT MANIFOLDS OF TWO-DIMENSIONAL MAPS" @default.
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- W2029226578 doi "https://doi.org/10.1142/s0218127411029604" @default.
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