8 papers
Brjuno condition through best approximations and the linearization problem
Nicolas Chevallier, João Lopes Dias, José Pedro Gaivão +2
We consider the classical analytic linearization problem for vector fields on the torus close to a constant vector field . Our goals are twofold. First, we provi…
Dirichlet improvability in -norms
Nikolay Moshchevitin, Nikita Shulga
For a norm on , we consider the set of -Dirichlet improvable numbers . In the most important case of being an -norm with , wh…
A note on uniform version of Littlewood inequality and Fibonacci numbers
Nikolay Moshchevitin
We give a simple proof of a recent result by J. Schleischitz dealing with a counterexample to the uniform Littlewood conjecture. Our construction is based on simple properties of F…
Bad approximability, bounded ratios and Diophantine exponents
Antoine Marnat, Nikolay Moshchevitin, Johannes Schleischitz
For a real matrix , we consider its sequence of best Diophantine approximation vectors , the sequences of its no…
Metric theory of inhomogeneous Diophantine approximations with a fixed matrix
Nikolay Moshchevitin, Vasiliy Neckrasov
In this paper we develop a metric theory of inhomogeneous Diophantine approximation for the case of a fixed matrix. We use transference principle to connect uniform Diophantine pro…
A note on general isolation result in Diophantine Approximation
Sergei Pitcyn, Nikolay Moshchevitin
In the present paper we give very simple general statements which deal with approximation of a real number by rationals and are related to isolation phenomenon. In particular we st…