Birkhoff sum project 2010

Research project

Birkhoff Sums Over the Golden Rotation

Office: SciCtr 434

Email: knill@math.harvard.edu

Update posted November 2016: Some notes [PDF]
and Slides [PDF] to a talk given at BU
in February 2015. In this project with Folkert Tangerman from Stony Brook we look at the Birkhoff sum _{n}/log(n)^{2}
is bounded. In the current work, we relate the boundedness of S_{n}/log(n)
to a limiting function f(x) obtained as a limiting difference
between consecutive continued fraction expansions. While the function
s_{n}(x) = S_{[x qn](alpha)/log(qn)} only converges weakly,
the sequence of functions
fconverges pointwise to a function f(x) on [0,1]. This project started during spring break 2010. Folkert visited Cambridge once in April. Otherwise we worked electronically or by phone. The paper got finalized during a meeting in New London (MA) on May 24, 2010. |

Questions and comments to knill@math.harvard.edu