# Generalized golden ratios of ternary alphabets

Vilmos Komornik; Anna Chiara Lai; Marco Pedicini

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 4, page 1113-1146
- ISSN: 1435-9855

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topKomornik, Vilmos, Lai, Anna Chiara, and Pedicini, Marco. "Generalized golden ratios of ternary alphabets." Journal of the European Mathematical Society 013.4 (2011): 1113-1146. <http://eudml.org/doc/277475>.

@article{Komornik2011,

abstract = {Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets
the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in dependence on the alphabets.},

author = {Komornik, Vilmos, Lai, Anna Chiara, Pedicini, Marco},

journal = {Journal of the European Mathematical Society},

keywords = {golden ratio; ternary alphabet; unique expansion; noninteger base; beta-expansion; greedy expansion; lazy expansion; univoque sequence; golden ratio; ternary alphabet; unique expansion; noninteger base; beta-expansion; greedy expansion; lazy expansion; univoque sequence; Sturmian sequences},

language = {eng},

number = {4},

pages = {1113-1146},

publisher = {European Mathematical Society Publishing House},

title = {Generalized golden ratios of ternary alphabets},

url = {http://eudml.org/doc/277475},

volume = {013},

year = {2011},

}

TY - JOUR

AU - Komornik, Vilmos

AU - Lai, Anna Chiara

AU - Pedicini, Marco

TI - Generalized golden ratios of ternary alphabets

JO - Journal of the European Mathematical Society

PY - 2011

PB - European Mathematical Society Publishing House

VL - 013

IS - 4

SP - 1113

EP - 1146

AB - Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets
the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in dependence on the alphabets.

LA - eng

KW - golden ratio; ternary alphabet; unique expansion; noninteger base; beta-expansion; greedy expansion; lazy expansion; univoque sequence; golden ratio; ternary alphabet; unique expansion; noninteger base; beta-expansion; greedy expansion; lazy expansion; univoque sequence; Sturmian sequences

UR - http://eudml.org/doc/277475

ER -

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