Birkhoff sum project 2010
The difference sum converges
The Birkhoff difference sum
Office: SciCtr 434


We see here the graphs of fn(x) for various n. We introduced the difference sum 
fn(x) = S[x qn](pn+1/qn+1) - S[x qn](pn/qn)
in our paper. The pn/qn are the convergents of the rotation number defined by the continued fraction expansion. In our case they are given by Fibonacci numbers. The pictures below show the graphs of the function fn for various n.
Questions and comments to knill@math.harvard.edu
Oliver Knill | Department of Mathematics | Harvard University