G-index, topological dynamics and the marker property

Given an action of a finite group G on topological space, we can define its index. The G-index roughly measures size the given G-space. We explore connections between theory and dynamics. For fixed-point free dynamical system, study ℤp-index set p-periodic points. find that growth is at most linear in p. As application, construct system which does not have marker property. This solves problem has been open for several years.