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We prove several results on (fractal) geometric properties of the classical Markov and Lagrange spectra. In particular, we prove that the Hausdorff dimensions of intersections of both spectra with half-lines always coincide, and we may assume any real value in the interval $[0, 1]$.
@article{10_4007_annals_2018_188_1_3,
author = {Carlos Gustavo Moreira},
title = {Geometric properties of the {Markov} and {Lagrange} spectra},
journal = {Annals of mathematics},
pages = {145--170},
publisher = {mathdoc},
volume = {188},
number = {1},
year = {2018},
doi = {10.4007/annals.2018.188.1.3},
mrnumber = {3815461},
zbl = {06890811},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.188.1.3/}
}
TY - JOUR AU - Carlos Gustavo Moreira TI - Geometric properties of the Markov and Lagrange spectra JO - Annals of mathematics PY - 2018 SP - 145 EP - 170 VL - 188 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.188.1.3/ DO - 10.4007/annals.2018.188.1.3 LA - en ID - 10_4007_annals_2018_188_1_3 ER -
%0 Journal Article %A Carlos Gustavo Moreira %T Geometric properties of the Markov and Lagrange spectra %J Annals of mathematics %D 2018 %P 145-170 %V 188 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.188.1.3/ %R 10.4007/annals.2018.188.1.3 %G en %F 10_4007_annals_2018_188_1_3
Carlos Gustavo Moreira. Geometric properties of the Markov and Lagrange spectra. Annals of mathematics, Tome 188 (2018) no. 1, pp. 145-170. doi: 10.4007/annals.2018.188.1.3
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