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June  2009, 2(2): 287-300. doi: 10.3934/dcdss.2009.2.287

Heaviness in symbolic dynamics: Substitution and Sturmian systems

David Ralston 1,

1. 

Department of Mathematics, The Ohio State University, 231 W. 18th Avenue, Columbus, OH 43210, United States

Received  February 2008 Revised  August 2008 Published  April 2009

Heaviness refers to a sequence of partial sums maintaining a certain lower bound and was recently introduced and studied in [11]. After a review of basic properties to familiarize the reader with the ideas of heaviness, general principles of heaviness in symbolic dynamics are introduced. The classical Morse sequence is used to study a specific example of heaviness in a system with nontrivial rational eigenvalues. To contrast, Sturmian sequences are examined, including a new condition for a sequence to be Sturmian.
Keywords: Heaviness, Morse Sequence., Sturmian Sequences.
Mathematics Subject Classification: Primary: 37B1.
Citation: David Ralston. Heaviness in symbolic dynamics: Substitution and Sturmian systems. Discrete and Continuous Dynamical Systems - S, 2009, 2 (2) : 287-300. doi: 10.3934/dcdss.2009.2.287
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