Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations

Robinson, James and Sharples, Nicholas ORCID: https://orcid.org/0000-0003-1722-5647 (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. ISSN 0022-0396 [Article] (doi:10.1016/j.jde.2013.02.012)

Preview

PDF - Final accepted version (with author's formatting) Download (287kB) | Preview

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.

Actions (login required)

View Item

Statistics

DownloadsShow export options

Export as CSVXMLJSON

Activity Overview

6 month trend

164Downloads

6 month trend

336Hits

Additional statistics are available via IRStats2.