3 citations · 3 across the 10 of their papers we have counts for
16 papers
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…
CayleyPy RL: Pathfinding and Reinforcement Learning on Cayley Graphs
A. Chervov, M. Obozov, A. Soibelman +31
This paper is the second in a series of studies on developing efficient artificial intelligence-based approaches to pathfinding on extremely large graphs (e.g. nodes) wit…
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…
Convergence of improper Iwasawa Continued Fractions
Anton Lukyanenko, Joseph Vandehey
We prove the convergence of a wide class of continued fractions, including generalized continued fractions over quaternions and octonions. Fractional points in these systems are no…
Projection theorems for linear-fractional families of projections
Anton Lukyanenko, Annina Iseli
Marstrand's theorem states that applying a generic rotation to a planar set before projecting it orthogonally to the -axis almost surely gives an image with the maximal poss…
Probabilistic motion planning for non-Euclidean and multi-vehicle problems
Anton Lukyanenko, Damoon Soudbakhsh
Trajectory planning tasks for non-holonomic or collaborative systems are naturally modeled by state spaces with non-Euclidean metrics. However, existing proofs of convergence for s…
Ergodicity of Iwasawa continued fractions via markable hyperbolic geodesics
Anton Lukyanenko, Joseph Vandehey
We prove the convergence and ergodicity of a wide class of real and higher-dimensional continued fraction algorithms, including folded and -type variants of complex, quaternioni…
Heisenberg quasiregular ellipticity
Katrin Fässler, Anton Lukyanenko, Jeremy T. Tyson
Following the Euclidean results of Varopoulos and Pankka--Rajala, we provide a necessary topological condition for a sub-Riemannian 3-manifold to admit a nonconstant quasiregul…
Quasiconvexity in the Heisenberg group
David A. Herron, Anton Lukyanenko, Jeremy T. Tyson
We show that if is a closed subset of the Heisenberg group whose vertical projections are nowhere dense, then the complement of is quasiconvex. In particular, closed sets w…
Separated Nets in Nilpotent Groups
Tullia Dymarz, Michael Kelly, Sean Li +1
In this paper we generalize several results on separated nets in Euclidean space to separated nets in connected simply connected nilpotent Lie groups. We show that every such group…
Intrinsic Diophantine approximation in Carnot groups and in the Siegel model of the Heisenberg group
Anton Lukyanenko, Joseph Vandehey
We initiate the study of an intrinsic notion of Diophantine approximation on a rational Carnot group . If has Hausdorff dimension , we show that its Diophantine exponent…
Quasiregular mappings on sub-Riemannian manifolds
Katrin Fassler, Anton Lukyanenko, Kirsi Peltonen
We study mappings on sub-Riemannian manifolds which are quasi-regular with respect to the Carnot-Caratheodory distances and discuss several related notions. On H-type Carnot groups…
Continued fractions on the Heisenberg group
Anton Lukyanenko, Joseph Vandehey
We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several…
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…
Bi-Lipschitz extension from boundaries of certain hyperbolic spaces
Anton Lukyanenko
Tukia and Vaisala showed that every quasi-conformal map of extends to a quasi-conformal self-map of . The restriction of the extended map to the upper half-space $…
On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target
Noel DeJarnette, Piotr Hajlasz, Anton Lukyanenko +1
We study the question: when are Lipschitz mappings dense in the Sobolev space ? Here denotes a compact Riemannian manifold with or without boundary, wh…