Adic dynamics on the Catalan graph

In this paper, we study the dynamics of the adic map on the Catalan graph. The Catalan graph is formed by taking the right half of the well-studied Pascal graph, and the Catalan numbers arise as path counts. For the adic map on the Catalan graph, the we show that the edge weights for invariant measu...

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Bibliographic Details
Published inDynamical systems (London, England) Vol. 39; no. 4; pp. 569 - 591
Main Authors Frick, Sarah, Ormes, Nicholas, Dolph, Toni
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.10.2024
Taylor & Francis Ltd
Subjects
Apexes
Dynamical systems
Graph theory
Online AccessGet full text
ISSN1468-9367
1468-9375
DOI10.1080/14689367.2024.2342083

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Summary:In this paper, we study the dynamics of the adic map on the Catalan graph. The Catalan graph is formed by taking the right half of the well-studied Pascal graph, and the Catalan numbers arise as path counts. For the adic map on the Catalan graph, the we show that the edge weights for invariant measures depend not only on the level, but also the index of the source and range vertices. This is in contrast to the Pascal adic systems and many other examples that have been explored. We prove a number of results about the dynamics and complexity of the associated measure-theoretic dynamical systems.
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ISSN:1468-9367
1468-9375
DOI:10.1080/14689367.2024.2342083