Cibles rétrécissantes de rayon $n^{-\frac{1}{d}}$ : propriété du logarithme

Benjamin Mussat (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

A translation on the d-dimensional torus $\mathbb{T}^d$ has the logarithm property if the Shrinking Target Property holds for the sequence of balls with radius $n^{-\frac{1}{d}}$. On $\mathbb{T}^1$ 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

Domaines: Systèmes dynamiques [math.DS]

Benjamin Mussat. Cibles rétrécissantes de rayon $n^{-\frac{1}{d}}$ : propriété du logarithme. 2010. ⟨hal-00574970⟩