Generalized golden ratios of ternary alphabets - Mathematics > Number TheoryReport as inadecuate




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Abstract: Expansions in noninteger bases often appear in number theory and probabilitytheory, and they are closely connected to ergodic theory, measure theory andtopology. For two-letter alphabets the golden ratio plays a special role: insmaller bases only trivial expansions are unique, whereas in greater basesthere exist nontrivial unique expansions. In this paper we determine thecorresponding critical bases for all three-letter alphabets and we establishthe fractal nature of these bases in function of the alphabets.



Author: Vilmos Komornik, Anna Chiara Lai, Marco Pedicini

Source: https://arxiv.org/







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