2015/12/10 by Hedenmalm, Haakan, Montes-Rodriguez, Alfonso
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1512.03228
We propose an extension of ergodic theory which focuses on the identification of ergodicity in terms of the uniqueness of the invariant measure. We first explain the concept for the doubling maps, which can be analyzed using Fourier methods. We then proceed to the Gauss-type maps of interest, of the form x↦ -β/x mod 2\mathbb Z on the symmetric interval [-1,1], for 0