Antoine Marnat

collaborators

2 papers

math.DS2026

Brjuno condition through best approximations and the linearization problem

Nicolas Chevallier, JoÃ£o Lopes Dias, JosÃ© Pedro GaivÃ£o +2

We consider the classical analytic linearization problem for vector fields on the torus $T^{d}$ close to a constant vector field $I ¨ $ . Our goals are twofold. First, we provi…

math.NT2026

Bad approximability, bounded ratios and Diophantine exponents

Antoine Marnat, Nikolay Moshchevitin, Johannes Schleischitz

For a real $m \times n$ matrix $I^¾$ , we consider its sequence of best Diophantine approximation vectors $x_{i} \in Z^{n}, i = 1, 2, 3, ...$ , the sequences of its no…