Shadowing for differential equations with grow-up
Dynamical Systems
2014-09-25 v1
Abstract
We consider the problem of shadowing for differential equations with grow-up. We introduce so-called nonuniform shadowing properties (in which size of the error depends on the point of the phase space) and prove for them analogs of shadowing lemma. Besides, we prove a theorem about weighted shadowing for flows. We compactify the system (using Poincare compactification, for example), apply the results about nonuniform or weighted shadowing to the compactified system, and then transfer the results back to the initial system using the decompactification procedure.
Cite
@article{arxiv.1409.6980,
title = {Shadowing for differential equations with grow-up},
author = {Alexey Osipov},
journal= {arXiv preprint arXiv:1409.6980},
year = {2014}
}
Comments
preprint, 19 pages, 3 figures