Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations
Article
Robinson, J. and Sharples, N. 2013. Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations. Journal of Differential Equations. 254, pp. 4144-4167. https://doi.org/10.1016/j.jde.2013.02.012
Type | Article |
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Title | Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations |
Authors | Robinson, J. and Sharples, N. |
Abstract | We provide a criterion for a generalised flow solution of a non-autonomous ordinary differential equation to avoid a subset of the phase space. This improves on that established by Aizenman for the autonomous case, where avoidance is guaranteed if the underlying vector field is sufficiently regular and the subset has sufficiently small box-counting dimension. We define the r-codimension print of a subset $S\subset \R^{n}\times [0,T]$, which is a subset of $(0,\infty]^{2}$ that encodes the dimension of S in a way that distinguishes spatial and temporal detail. We prove that the subset S is avoided by a generalised flow solution with underlying vector field in $L^{p}(0, T; L^{q}(R^{n}))$ if the Holder conjugates (q^{*}; p^{*}) are in the r-codimension print of S. |
Publisher | Elsevier |
Journal | Journal of Differential Equations |
ISSN | 0022-0396 |
Publication dates | |
Online | 05 Mar 2013 |
15 May 2013 | |
Publication process dates | |
Deposited | 15 Oct 2015 |
Accepted | 04 Dec 2012 |
Output status | Published |
Accepted author manuscript | |
Web address (URL) | http://www.sciencedirect.com/science/article/pii/S0022039613000879 |
Digital Object Identifier (DOI) | https://doi.org/10.1016/j.jde.2013.02.012 |
Language | English |
https://repository.mdx.ac.uk/item/85zqq
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