DCDS
Rigorous high-dimensional shadowing using containment: The general case
Wayne B. Hayes Kenneth R. Jackson Carmen Young
A shadow is an exact solution to an iterated map that remains close to an approximate solution for a long time. An elegant geometric method for proving the existence of shadows is called containment, and it has been proven previously in two and three dimensions, and in some special cases in higher dimensions. This paper presents the general proof using tools from differential and algebraic topology and singular homology.
keywords: reliable simulation. Nonlinear dynamical systems shadowing

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