2005/10/18 by Alexei G. Myasnikov, Myasnikov, Alexei G., Vladimir Shpilrain +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #math.GR #math.MG
paper · pdf · doi:10.48550/arxiv.math/0510398
11 pages
arxiv created 2005/10/18 · arxiv updated 2009/12/01
Study of the dynamics of automorphisms of a group is usually focused on their growth and/or finite orbits, including fixed points. In this paper, we introduce properties of a different kind; using somewhat informal language, we call them metric properties. Two principal characteristics of this kind are called here the "curl" and the "flux"; there seems to be very little correlation between these and the growth of an automorphism, which means they are likely to be an essentially new tool for studying automorphisms. We also observe that our definitions of the curl and flux are sufficiently general to be applied to mappings of arbitrary metric spaces.