2019/04/22 by Hochman, Michael, Rapaport, Ariel · 4 citations
#28A80 #37C45 #37F35 #Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1904.09812
We prove that if μ is a self-affine measure in the plane whose defining IFS acts totally irreducibly on \mathbbRP1 and satisfies an exponential separation condition, then its dimension is equal to its Lyapunov dimension. We also treat a class of reducible systems. This extends our previous work on the subject with Bárány to the overlapping case.