3 papers
math.DS2025
Products of exact dynamical systems and Lorentzian continued fractions
Brandon G. Barreto-Rosa, Jean-Philippe Burelle, Anton Lukyanenko +1
We describe a new continued fraction system in Minkowski space , proving convergence, ergodicity with respect to an explicit invariant measure, and Lagrange's theo…
math.DS2023
Serendipitous decompositions of higher-dimensional continued fractions
Anton Lukyanenko, Joseph Vandehey
We prove a suite of dynamical results, including exactness of the transformation and piecewise-analyticity of the invariant measure, for a family of continued fraction systems, inc…
math.GT2012
Quasi-isometric co-Hopficity of non-uniform lattices in rank-one semi-simple Lie groups
Ilya Kapovich, Anton Lukyanenko
We prove that if is a non-uniform lattice in a rank-one semi-simple Lie group $\ne Isom(\H^2_\R)$ then is quasi-isometrically co-Hopf. This means that every quasi-isometric…