Cibles rétrécissantes de rayon n⁻¹/ᵈ: propriété du logarithme
Mussat, Benjamin
Original · EN
A translation on the d-dimensional torus Tᵈ has the logarithm property if the Shrinking Target Property holds for the sequence of balls with radius n⁻¹/ᵈ. On T¹ 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
English translation
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