High-order Bisection method for computing invariant manifolds of two-dimensional maps

Document Type

Article

Publication Date

1-1-2011

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 CatmullRom 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. © 2011 World Scientific Publishing Company.

Identifier

80052184993 (Scopus)

Publication Title

International Journal of Bifurcation and Chaos

External Full Text Location

https://doi.org/10.1142/S0218127411029604

ISSN

02181274

First Page

2017

Last Page

2042

Issue

7

Volume

21

Grant

DMS-0639270

Fund Ref

National Science Foundation

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