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Tracking Invariant Manifolds

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Book cover Multiple Time Scale Dynamics

Part of the book series: Applied Mathematical Sciences ((AMS,volume 191))

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Abstract

The main goal of this chapter is to discuss the tracking of invariant manifolds when they transition from a fast to a slow motion and vice versa. That is, we would like to understand how trajectories or more general objects enter and leave the vicinity of a normally hyperbolic critical manifold. The main application is to show how the geometric theory of fast–slow systems can be used to prove the persistence of candidate orbits for \(0 <\varepsilon \ll 1\).

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  1. Institute for Analysis and Scientific Computing, Vienna University of Technology, Vienna, Austria

    Christian Kuehn

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Kuehn, C. (2015). Tracking Invariant Manifolds. In: Multiple Time Scale Dynamics. Applied Mathematical Sciences, vol 191. Springer, Cham. https://doi.org/10.1007/978-3-319-12316-5_6

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