Open AccessOn the quadratic Lagrange spectrum
Author(s) -
Yann Bugeaud
Publication year - 2013
Publication title -
mathematische zeitschrift
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.38
H-Index - 66
eISSN - 1432-1823
pISSN - 0025-5874
DOI - 10.1007/s00209-013-1230-1
Subject(s) - mathematics , quadratic equation , spectrum (functional analysis) , action (physics) , orbit (dynamics) , irrational number , pure mathematics , mathematical analysis , combinatorics , geometry , quantum mechanics , physics , engineering , aerospace engineering
We study the quadratic Lagrange spectrum defined by Parkkonen and Paulin by considering the approximation by elements of the orbit of a given real quadratic irrational number for the action by homographies and anti-homographies of $$PSL_2(\mathbf{Z})$$PSL2(Z) on $$\mathbf{R}\cup \{\infty \}$$R∪{∞}. Our approach is based on the theory of continued fractions.
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