19 citations · 104 across the 41 of their papers we have counts for
8 papers · 1 filter
Diophantine properties of IETs and general systems: Quantitative proximality and connectivity
Michael Boshernitzan, Jon Chaika
We present shrinking targets results for general systems with the emphasis on applications for IETs (interval exchange transformations) , . In particular, we prove…
Borel-Cantelli sequences
Michael Boshernitzan, Jon Chaika
A sequence in is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers with $\underset{i=1}{\overset{\infty…
There exists a topologically mixing IET
Jon Chaika
This paper uses a construction of M. Keane to show that there exists a topologically mixing interval exchange transformation.
Shrinking targets for IETs: Extending a theorem of Kurzweil
Jon Chaika
This paper proves shrinking target results for IETs. Let {a_1\geq a_2 \geq...} be a sequence of positive real numbers with divergent sum. Then for almost every IET T, the limsup of…
On the Frequency of Balanced Times in Cylinder Flows
Jon Chaika, David Ralston
Given an irrational alpha and an x in the unit interval, the set of balanced times, for which the same number of (k*alpha+x) (modulo one) are less than or equal to one half as are…
The densest sequence in the unit circle
Michael Boshernitzan, Jon Chaika
We exhibit the densest sequence on the unit circle R/Z, x_k= log(2k-1)/log(2) (mod 1).