相关论文: On uniform Diophantine exponents of lattices

In this paper we describe the spectrum of values of weak uniform Diophantine exponents of lattices in arbitrary dimension.

We describe the spectrum of ordinary Diophantine exponents for $d$-dimensional lattices. The result reduces the problem to two-dimensional case and uses argument of metric theory.

In this paper we introduce the notion of a weak uniform Diophantine exponent of a real number and obtain the complete description of the spectrum of its values.

In this paper we define Diophantine exponents of lattices and investigate some of their properties. We prove transference inequalities and construct some examples with the help of Schmidt's subspace theorem.

In this paper we prove that uniform Diophantine exponents of lattices attain only trivial values.

In this paper we give a survey of what is currently known about Diophantine exponents of lattices and propose several problems.

We study properties of Diophantine exponents of lattices and so-called related "weak" uniform approximations introduced in recent papers by Oleg German, in the simplest two-dimensional case. In contrast to the multidimensional case, in the…

In this paper we prove an existence theorem concerning linear forms of a given Diophantine type and apply it to study the structure of the spectrum of lattice exponents.

In this paper we prove an inequality for individual and uniform Diophantine exponents in the case of simultaneous approximation. This inequality is better than Jarnik's for small values of the uniform exponent.

Diophantine exponents are ones of the simplest quantitative characteristics responsible for the approximation properties of linear subspaces of a Euclidean space. This survey is aimed at describing the current state of the area of…

Recent years have seen very important developments at the interface of Diophantine approximation and homogeneous dynamics. In the first part of the paper we give a brief exposition of a dictionary developed by Dani and Kleinbock-Margulis…

In this paper we prove transference inequalities for regular and uniform Diophantine exponents in the weighted setting. Our results generalize the corresponding inequalities that exist in the `non-weighted' case.

We survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.

The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.

We obtain some new inequalities between the ordinary and the uniform Diophantine exponents for simultaneous Diophantine approximation to four real numbers.

We place the theory of metric Diophantine approximation on manifolds into a broader context of studying Diophantine properties of points generic with respect to certain measures on $\Bbb R^n$. The correspondence between multidimensional…

We extend the Khintchine transference inequalities, as well as a homogeneous-inhomogeneous transference inequality for lattices, due to Bugeaud and Laurent, to a weighted setting. We also provide applications to inhomogeneous Diophantine…

We aim to fill a gap in the proof of an inequality relating two exponents of uniform Diophantine approximation stated in a paper by Bugeaud. We succeed to verify the inequality in several instances, in particular for small dimension.…

In this paper, a necessary and sufficient condition for the stability of Lyapunov exponents of linear differential system are proved in the sense that the equations satisfy the weaker form of integral separation instead of its classical…

This paper is devoted to give a complete unified study of several weak forms of $\ddb-$Lemma on compact complex manifolds.