American Institute of Mathematical Sciences

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May  2008, 9(3&4, May): 493-516. doi: 10.3934/dcdsb.2008.9.493

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, Canada
2. 

Dipartimento di Sistemi e Informatica, Università di Firenze, Via di S. Marta 3, 50139 Firenze

Received  January 2007 Revised  June 2007 Published  February 2008

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.
Keywords: almost periodic coefficients., projective flows, minimal subsets, Li-Yorke chaos.
Mathematics Subject Classification: Primary: 37B55, 37D25, 34C2.
Citation: Kristian Bjerklöv, Russell Johnson. Minimal subsets of projective flows. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 493-516. doi: 10.3934/dcdsb.2008.9.493
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