2016/09/06 by Boroński, Jan P., Kupka, Jiří, Oprocha, Piotr · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1609.01631
We prove that there exists a topologically mixing homeomorphism which is completely scrambled. We also prove that for any integer n≥ 1 there is a continuum of topological dimension n supporting a transitive completely scrambled homeomorphism, and n-dimensional compactum supporting a weakly mixing completely scrambled homeomorphism. This solves a 15 year old open problem.