Generalized golden ratios of ternary alphabets

Komornik, 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 -