Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Lukyanenko, Anton"'
Autor:
Lukyanenko, Anton, Vandehey, Joseph
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, including specific examples over reals, complex numbers, quaternions, oct
Externí odkaz:
http://arxiv.org/abs/2303.02249
Autor:
Lukyanenko, Anton, Vandehey, Joseph
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 not bounded away from the unit sphere, so that the iteration map is not
Externí odkaz:
http://arxiv.org/abs/2205.12801
Autor:
Lukyanenko, Anton, Iseli, Annina
Marstrand's theorem states that applying a generic rotation to a planar set $A$ before projecting it orthogonally to the $x$-axis almost surely gives an image with the maximal possible dimension $\min(1, \dim A)$. We first prove, using the transversa
Externí odkaz:
http://arxiv.org/abs/2112.12274
Autor:
Lukyanenko, Anton, Soudbakhsh, Damoon
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 sample-based motion planners only consider the setting of Euclidean sta
Externí odkaz:
http://arxiv.org/abs/2108.03191
Autor:
Lukyanenko, Anton, Soudbakhsh, Damoon
Publikováno v:
In Robotics and Autonomous Systems October 2023 168
Autor:
Lukyanenko, Anton, Vandehey, Joseph
We prove the convergence and ergodicity of a wide class of real and higher-dimensional continued fraction algorithms, including folded and $\alpha$-type variants of complex, quaternionic, octonionic, and Heisenberg continued fractions, which we combi
Externí odkaz:
http://arxiv.org/abs/1805.09312
Following the Euclidean results of Varopoulos and Pankka--Rajala, we provide a necessary topological condition for a sub-Riemannian 3-manifold $M$ to admit a nonconstant quasiregular mapping from the sub-Riemannian Heisenberg group $\mathbb{H}$. As a
Externí odkaz:
http://arxiv.org/abs/1610.07665
We show that if $A$ is a closed subset of the Heisenberg group whose vertical projections are nowhere dense, then the complement of $A$ is quasiconvex. In particular, closed sets which are null sets for the cc-Hausdorff $3$-measure have quasiconvex c
Externí odkaz:
http://arxiv.org/abs/1609.07749
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 $G$ contains separated nets that are not biLipschitz equivalent. We d
Externí odkaz:
http://arxiv.org/abs/1608.08572
Intrinsic Diophantine approximation in Carnot groups and in the Siegel model of the Heisenberg group
Autor:
Lukyanenko, Anton, Vandehey, Joseph
We initiate the study of an intrinsic notion of Diophantine approximation on a rational Carnot group $G$. If $G$ has Hausdorff dimension $Q$, we show that its Diophantine exponent is equal to $(Q+1)/Q$, generalizing the case $G=\mathbb R^n$. We furth
Externí odkaz:
http://arxiv.org/abs/1510.06033