Rigorous high-dimensional shadowing using containment: The general case

Wayne B. Hayes; Kenneth R. Jackson; Carmen Young

doi:10.3934/dcds.2006.14.329

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2006, Volume 14, Issue 2: 329-342. Doi: 10.3934/dcds.2006.14.329

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Rigorous high-dimensional shadowing using containment: The general case

1.
Dept. of Computer Science, University of California, Irvine, Irvine, California 92697-3425
2.
Computer Science Dept., University of Toronto, Toronto, Ontario M5S 3G4
3.
The Fields Institute, 222 College Street, Toronto, ON M5T 3J1

Received: October 31, 2004

Revised: May 31, 2005

Published: March 2006

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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.

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Mathematics Subject Classification: Primary: 57R19, 65G20; Secondary: 57R50, 65L70.

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