11 citations · 43 across the 30 of their papers we have counts for
4 papers · 2 filters
On two-dimensional continued fractions for the integer hyperbolic matrices with small norm
Oleg Karpenkov
In this note we classify two-dimensional continued fractions for cubic irrationalities constructed by matrices with not large norm (). The classification is based on the…
On tori triangulations associated with two-dimensional continued fractions of cubic irrationalities
Oleg Karpenkov
We show several properties related to the structure of the family of classes of two-dimensional periodic continued fractions. This approach to the study of the family of classes of…
Continued fractions and the second Kepler law
Oleg Karpenkov
In this paper we introduce a link between geometry of ordinary continued fractions and trajectories of points that moves according to the second Kepler law. We expand geometric int…
Rational approximation of the maximal commutative subgroups of GL(n,R)
O. Karpenkov, A. Vershik
How to find "best rational approximations" of maximal commutative subgroups of GL(n,R)? In this paper we pose and make first steps in the study of this problem. It contains both cl…