 

Andrew Haas
An ergodic sum related to the approximation by continued fractions


Published: 
July 21, 2005 
Keywords: 
Continued fractions, metric theory, interval maps 
Subject: 
11J70, 11J83, 37E05 


Abstract
To each irrational number x is associated an infinite sequence of rational fractions
(p_{n}/q_{n}), known as the convergents of x. Consider the functions
q_{n} q_{n}xp_{n} =θ_{n}(x).
We shall primarily be concerned with the computation, for almost all real x, of the ergodic sum
lim_{n→∞} (1/n)∑_{k=1}^{n}logθ_{k}(x)= 1(1/2)log 2≈ 1.34657.


Author information
Department of Mathematics, The University of Connecticut, Storrs, CT. 062693009
haas@math.uconn.edu

