Shifts of finite type and random substitutions
| Autor: | Philipp Gohlke, Dan Rust, Timo Spindeler |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Logarithm Applied Mathematics Substitution (logic) Dynamical Systems (math.DS) Topological entropy Type (model theory) 37B10 37A50 37B40 52C23 shifts of finite type 01 natural sciences Random substitutions 010101 applied mathematics Set (abstract data type) Dimension (vector space) topological entropy FOS: Mathematics Discrete Mathematics and Combinatorics 0101 mathematics Mathematics - Dynamical Systems Positive real numbers Topological conjugacy Analysis Mathematics |
| ISSN: | 1553-5231 |
| Popis: | We prove that every topologically transitive shift of finite type in one dimension is topologically conjugate to a subshift arising from a primitive random substitution on a finite alphabet. As a result, we show that the set of values of topological entropy which can be attained by random substitution subshifts contains the logarithm of all Perron numbers and so is dense in the positive real numbers. We also provide an independent proof of this density statement using elementary methods. |
| Databáze: | OpenAIRE |
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