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Expansions in Complex Bases

  Published:2007-09-01
 Printed: Sep 2007
  • Vilmos Komornik
  • Paola Loreti
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Abstract

Beginning with a seminal paper of R\'enyi, expansions in noninteger real bases have been widely studied in the last forty years. They turned out to be relevant in various domains of mathematics, such as the theory of finite automata, number theory, fractals or dynamical systems. Several results were extended by Dar\'oczy and K\'atai for expansions in complex bases. We introduce an adaptation of the so-called greedy algorithm to the complex case, and we generalize one of their main theorems.
Keywords: non-integer bases, greedy expansions, beta-expansions non-integer bases, greedy expansions, beta-expansions
MSC Classifications: 11A67, 11A63, 11B85 show english descriptions Other representations
Radix representation; digital problems {For metric results, see 11K16}
Automata sequences
11A67 - Other representations
11A63 - Radix representation; digital problems {For metric results, see 11K16}
11B85 - Automata sequences
 

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