Abstract: Fix α ∈ (0,1}, and consider a sequence of partitions of the interval, starting with the trivial one, {[0,1]}, and where the (n+1)st partition is obtained by splitting all maximal intervals in the nth into two, in the ratio α : 1-α.
The question posed to Kakutani: does the set of endpoints of the nth partition become uniformly distributed in the limit? We will consider the answer to this question, and some of its generalisations/variations: whether its more dimensions, intervals or randomness, there appears to be no limit to the questions one can ask. Naturally, some are open. This is joint work with Mark Pollicott.
The α-Kakutani equidistribution problem, and friends
18.11.2022 14:00 - 15:00
Organiser:
H. Bruin
Location: