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Numerical analysis of degenerate connecting orbits for maps. (English) Zbl 1129.37353

Summary: This paper contains a survey of numerical methods for connecting orbits in discrete dynamical systems. Special emphasis is put on degenerate cases where either the orbit loses transversality or one of its endpoints loses hyperbolicity. Numerical methods that approximate the connecting orbits by finite orbit sequences are described in detail and theoretical results on the error analysis are provided. For most of the degenerate cases we present examples and numerical results that illustrate the applicability of the methods and the validity of the error estimates.

MSC:

37M20 Computational methods for bifurcation problems in dynamical systems
37G99 Local and nonlocal bifurcation theory for dynamical systems
65P99 Numerical problems in dynamical systems
37C29 Homoclinic and heteroclinic orbits for dynamical systems
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory

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