Cibles r\'etr\'ecissantes de rayon $n^{-\frac{1}{d}}$ : propri\'et\'e du logarithme
Dynamical Systems
2011-03-24 v1
Abstract
A translation on the d-dimensional torus has the logarithm property if the Shrinking Target Property holds for the sequence of balls with radius . On every irrational translations has this property. In higher dimension, we give criterions based upon an unusual Diophantine type. In the two dimensional torus, we construct counter examples to the logarithm with translations vectors of arbitrary small Diophantine type and example of logarithm property with Liouvillian vector
Keywords
Cite
@article{arxiv.1103.4594,
title = {Cibles r\'etr\'ecissantes de rayon $n^{-\frac{1}{d}}$ : propri\'et\'e du logarithme},
author = {Benjamin Mussat},
journal= {arXiv preprint arXiv:1103.4594},
year = {2011}
}