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Hierarchical structures in Sturmian dynamical systems

✍ Scribed by Daniel Lenz

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
367 KB
Volume
303
Category
Article
ISSN
0304-3975

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✦ Synopsis

The paper is concerned with hierarchical structures in subshifts over a ΓΏnite alphabet. In particular, we present a hierarchy-based approach to Sturmian systems. This approach is then used to characterize the linearly repetitive Sturmian systems (among the Sturmian systems) by uniform positivity of certain weights. More generally, we discuss various bounds on weights and their relationship.

Finally, we combine hierarchies and bounds on weights to study a thermodynamic formalism for lattice gas models associated to arbitrary linearly repetitive subshifts.

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## _A We consider a dynamical system containing a large number of elements which can be in different states. In order to define a hierarchical partition of the system, strongly coupled states are put together creating groups of states. To each group is associated a single global variable. For such