Uncomputably noisy ergodic limits
Logic
2015-11-03 v2 Dynamical Systems
Abstract
V'yugin has shown that there are a computable shift-invariant measure on Cantor space and a simple function f such that there is no computable bound on the rate of convergence of the ergodic averages A_n f. Here it is shown that in fact one can construct an example with the property that there is no computable bound on the complexity of the limit; that is, there is no computable bound on how complex a simple function needs to be to approximate the limit to within a given epsilon.
Keywords
Cite
@article{arxiv.1105.0663,
title = {Uncomputably noisy ergodic limits},
author = {Jeremy Avigad},
journal= {arXiv preprint arXiv:1105.0663},
year = {2015}
}