Geometric Singular Perturbation Theory Beyond the Standard Form by Martin Wechselberger

Author:Martin Wechselberger
Language: eng
Format: epub, pdf
ISBN: 9783030363994
Publisher: Springer International Publishing

4.2.1 Comparison with the Standard Case

The corresponding standard k-dimensional desingularised problem (4.20) is given by

(4.23)

Note that along F. Hence locally near F, the critical manifold has to be studied in a coordinate chart that includes at least one fast coordinate y i, 1 ≤ i ≤ (n − k). The regular jump point condition (4.22) for a point z ∈ F becomes

(4.24)

Near jump points, solutions have the possibility to switch from the slow to the fast time scale or vice versa. The corresponding standard results which describe the flow near jump points for ε ≠ 0 can be found in Sect. 4.5. These local results apply directly to the general setting through (local) equivalence.

Remark 4.6

In the case of a normally hyperbolic manifold, the critical manifold is a graph y = Y 0(x) over the slow variable base and the desingularised problem (4.23) in this slow coordinate chart is simply given by

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.