The numerical detection of connecting orbits | Zendy

Michael Dellnitz | Zendy; Oliver Junge | Zendy; Bianca Thiere | Zendy

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The numerical detection of connecting orbits

Author(s) -

Michael Dellnitz,

Oliver Junge,

Bianca Thiere

Publication year - 2001

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2001.1.125

Subject(s) - invariant (physics) , computation , mathematics , dimension (graph theory) , set (abstract data type) , periodic orbits , dynamical systems theory , computer science , algorithm , pure mathematics , mathematical analysis , physics , mathematical physics , quantum mechanics , programming language

We present a new technique for the numerical detection and localization of connecting orbits between hyperbolic invariant sets in parameter dependent dynamical systems. This method is based on set-oriented multilevel methods for the computation of invariant manifolds and it can be applied to systems of moderate dimension. The main idea of the algorithm is to detect intersections of coverings of the stable and unstable manifolds of the invariant sets on different levels of the approximation. We demonstrate the applicability of the new method by three examples.

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