中科院数学与系统科学研究院数学研究所学术报告动力系统研讨班摘 要：
摘 要：Let \nu be a Bernoulli measure on a fractal in R^d generated
by a finite collection of contracting similarities with no rotations and
with rational coefficients; for instance, the usual coin tossing measure
on Cantor's middle thirds set. Let a_t = diag (e^t ,..., e^t , e^-dt ), let U
be its expanding horospherical group, which we identify with R^d ,
and let \bar \nu be the pushforward of \nu onto the space of lattices
SL_d+1 (R)/SL_d+1 (Z), via the orbit map of the identity coset under
U. In joint work in progress with Khalil and Luethi, we show that the
pushforward of \bar \nu under a_t equidistributes as t tends to infinity,
as do the pushforwards under more general one parameter subgroups.
This generalizes a previous result of Khalil and Luethi. I will discuss
some Diophantine applications and some probabilistic ideas used in
the proof.
