糖心视频

The mass transference principle of Beresnevich and Velani is a powerful mechanism for determining the Hausdorff dimension/measure of sets that arise naturally in classical Diophantine approximation. However, in the setting of dynamical Diophantine approximation, this principle often fails to apply effectively, as the radii of the balls defining the dynamical sets generally depend on the orbit of the point itself.

In this talk, I will present a dimensional mass transference principle that enables us to recover and extend classical results on shrinking target problems, particularly for the β-transformation and the Gauss map. Moreover, our result shows that the corresponding sets have large intersection properties. I will also use a simple example to illustrate our method and, through it, explain the connection between shrinking target problems and thermodynamic formalism.