Minimal subsets of projective flows

Kristian Bjerklöv; Russell Johnson

doi:10.3934/dcdsb.2008.9.493

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2008, Volume 9, Issue 3&4: 493-516. Doi: 10.3934/dcdsb.2008.9.493

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Minimal subsets of projective flows

Kristian Bjerklöv^1, and
Russell Johnson^2,

1.
Department of Mathematics and Statistics, Queen's University, Kingston, ON Canada K7L 3N6
2.
Dipartimento di Sistemi e Informatica, Università di Firenze, Via di S. Marta 3, 50139 Firenze

Received: December 31, 2006

Revised: May 31, 2007

Published: April 2008

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Abstract

We study the minimal subsets of the projective flow defined by a two-dimensional linear differential system with almost periodic coefficients. We show that such a minimal set may exhibit Li-Yorke chaos and discuss specific examples in which this phenomenon is present. We then give a classification of these minimal sets, and use it to discuss the bounded mean motion property relative to the projective flow.

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Mathematics Subject Classification: Primary: 37B55, 37D25, 34C27.

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