Zoom, Online seminar
(線上演講 Zoom)
Uniform Approximation Problems of Expanding Markov Map
Yubin He (South China University of Technology)
Abstract
Let
be an expanding Markov map of the interval
with a finite partition. Let
be an invariant Gibbs measure associated with a Hölder continuous potential
. In this talk, we investigate the size of the uniform approximation set
%3A%3D%5C%7By%20%5Cin%20%5B0%2C%201%5D%3A%20%5Cforall%20N%20%5Cgg%201%2C~%5Cexists%20n%20%5Cleq%20N%2C%20%5Ctext%7B%20such%20that%20%7D%20%7CT%5En%20x%20-%20y%7C%20%3C%20N%5E%7B-%5Ckappa%7D%5C%7D%2C%24%24&chf=bg,s,333333&chco=ffffff)
where
and
. The critical value of
such that
%20%3D%201%24&chf=bg,s,333333&chco=ffffff)
for
is proven to be
, where
and
is the Gibbs measure associated with the potential
. Moreover, when
>1/
, we show that for
-a.e.~
, the Hausdorff dimension of
%24%20&chf=bg,s,333333&chco=ffffff)
agrees with the multifractal spectrum of
.
Meeting Link
https://us02web.zoom.us/j/82058526043?pwd=Z0QzVXZVNDRTRkhJMG4rQ0dlSlkzUT09
