2018/08/01 by Bozgan, Francisc, Sanchez, Anthony, Silva, Cesar E. +3
#20M99 (Secondary) #37A05 (Primary) 37A40 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1808.00483
This paper studies the notion of W-measurable sensitivity in the context of semigroup actions. W-measurable sensitivity is a measurable generalization of sensitive dependence on initial conditions. In 2012, Grigoriev et. al. proved a classification result of conservative ergodic dynamical systems that states all are either W-measurably sensitive or act by isometries with respect to some metric and have refined structure. We generalize this result to a class of semigroup actions. Furthermore, a counterexample is provided that shows W-measurable sensitivity is not preserved under factors. We also consider the restriction of W-measurably sensitive semigroup actions to sub-semigroups and show that the restriction remains W-measurably sensitive when the sub-semigroup is large enough (e.g. when the sub-semigroups are syndetic or thick).