Rigorous high-dimensional shadowing using containment: The general case
Wayne B. Hayes - Dept. of Computer Science, University of California, Irvine, Irvine, California 92697-3425, United States (email)
Abstract: 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: Nonlinear dynamical systems, shadowing, reliable simulation.
Received: November 2004; Revised: June 2005; Published: November 2005.
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