# American Institute of Mathematical Sciences

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

## Heaviness in symbolic dynamics: Substitution and Sturmian systems

 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.
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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