Properties of expansions in complex bases
Vilmos Komornik, Paola Loreti
TL;DR
This paper explores the properties of number expansions in complex and negative bases, extending previous research on noninteger positive bases to more general base systems, revealing new topological and combinatorial characteristics.
Contribution
It introduces new analyses of expansions in complex and negative bases, broadening the understanding of their topological and combinatorial properties beyond positive bases.
Findings
Extended studies to complex and negative bases
Identified new topological properties of these expansions
Analyzed combinatorial structures of base expansions
Abstract
Expansions in noninteger positive bases have been intensively investigated since the pioneering works of R\'enyi (1957) and Parry (1960). The discovery of surprising unique expansions in certain noninteger bases by Erd\H os, Horv\'ath and Jo\'o (1991) was followed by many studies aiming to clarify the topological and combinatorial nature of the sets of these bases. In the present work we extend some of these studies to more general, negative or complex bases.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Mathematical Dynamics and Fractals