TY - JOUR
T1 - Some metric properties of automorphisms of groups
AU - Myasnikov, Alexei G.
AU - Shpilrain, Vladimir
PY - 2006/10/15
Y1 - 2006/10/15
N2 - 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.
AB - 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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U2 - 10.1016/j.jalgebra.2005.10.001
DO - 10.1016/j.jalgebra.2005.10.001
M3 - Article
AN - SCOPUS:33748034078
SN - 0021-8693
VL - 304
SP - 782
EP - 792
JO - Journal of Algebra
JF - Journal of Algebra
IS - 2
ER -