Intrinsic Diophantine approximation on triadic Cantor set: the divergence theory
Ergodic Theory and Dynamical Systems Seminar
4th February 2021, 2:00 pm – 3:00 pm
Online via Zoom, (if interested, please email one of the organisers to gain access to the Zoom link)
In this talk, we will discuss a partial result about the intrinsic Diophantine approximation on triadic Cantor, i.e. approximate the points in triadic Cantor set by rational numbers inside the triadic Cantor set. Instead of the usual height of a rational number, we use a formal height of it obtained from its periodic triadic expansion. Then a Khintchine type result for the intrinsic approximation on the triadic Cantor set is obtained by using this new height which implies the divergence theory of the intrinsic approximation. The convergence theory is still open which is related to the cardinality of the reduced rational numbers in the triadic Cantor set with a prescribed range of their denominators.