Work

(S,w)-Gap Shifts and Their Entropy

Year: 2025

Type: article

Abstract: The S-gap shifts have a dynamically and combinatorially rich structure. Dynamical properties of the S-gap shift can be related to the properties of the set S. There is a well known formula for the entropy of an S-gap shift. Fix a point w of the full shift on {1,2,…,k}. We introduce the (S,w)-gap shift which is a generalization of the S-gap shift consisting of sequences over the alphabet {0,1,…,k} in which any two 0's are separated by a word u appearing in w with length in S. We extend the formula for the entropy of the S-gap shift to a formula describing the entropy of this new class of shift spaces. Additionally, we investigate the dynamical properties including irreducibility and mixing of this generalization of the S-gap shift.

Source: The PUMP Journal of Undergraduate Research

DOI: 10.46787/pump.v8i.4115

Authors: Cristian Ramirez, Amy Somers

Institutions: University of California, Berkeley, University of California, Santa Barbara

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Ohio State University

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