منابع مشابه
On the quadratic Lagrange spectrum
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 PSL2(Z) on R ∪ {∞}. Our approach is based on the theory of continued fractions.
متن کاملLagrange, central norms, and quadratic Diophantine equations
As is often the case, some results get rediscovered over time. In particular, some rather striking results of Lagrange are often recreated. For instance, in [6], a result pertaining to the Pell equation for a prime discriminant was recast in the light of nonabelian cohomology groups. Yet, in [1], the authors acknowledged the fact that the result “has been discovered before,” and provided an ele...
متن کاملMarkoff-lagrange Spectrum and Extremal Numbers
Let γ = (1+ √ 5)/2 denote the golden ratio. H. Davenport and W. M. Schmidt showed in 1969 that, for each non-quadratic irrational real number ξ, there exists a constant c > 0 with the property that, for arbitrarily large values of X , the inequalities |x0| ≤ X, |x0ξ − x1| ≤ cX , |x0ξ − x2| ≤ cX admit no non-zero solution (x0, x1, x2) ∈ Z. Their result is best possible in the sense that, convers...
متن کاملDynamical generalizations of the Lagrange spectrum
We compute two invariants of topological conjugacy, the upper and lower limits of the inverse of Boshernitzan's ne n , where e n is the smallest measure of a cylinder of length n, for three families of symbolic systems, the natural codings of rotations and three-interval exchanges and the Arnoux-Rauzy systems. The sets of values of these invariants for a given family of systems generalize the L...
متن کاملLocal Interpolation by a Quadratic Lagrange Finite Element in 1d
We analyse the error of interpolation of functions from the space H(a, c) in the nodes a < b < c of a regular quadratic Lagrange finite element in 1D by interpolants from the local function space of this finite element. We show that the order of the error depends on the way in which the mutual positions of nodes a, b, c change as the length of interval [a, c] approaches zero.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2017
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-017-1964-2