Some metric properties of automorphisms of groups

Details Some metric properties of automorphisms of groups Some metric properties of automorphisms of groups

2005-10-18

arxiv.org/abs/math/0510398v1

Mathematics

Group Theory

11 pages

Scientific paper

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.

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