Periodicity of Rauzy scheme and substitutional systems
Abstract
In the paper the notion of {\em Rauzy scheme} is introduced. From Rauzy graph Rauzy Scheme can be obtaining by uniting sequence of vertices of ingoing and outgoing degree 1 by arches. This notion is a tool to describe Rauzy graph behavior. For morphic superword we prove periodicity of Rauzy schemes. This is generalization of fact that quadratic irrationals have periodic chain fractions.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2011
- DOI:
- 10.48550/arXiv.1107.0185
- arXiv:
- arXiv:1107.0185
- Bibcode:
- 2011arXiv1107.0185K
- Keywords:
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- Mathematics - Dynamical Systems;
- Mathematics - Combinatorics
- E-Print:
- in Russian