A note on the dynamics of linear automorphisms of a measure convolution algebra

2013/04/26 by Alexandre Baraviera, Baraviera, Alexandre, Elismar R. Oliveira +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1304.7182

14 pages

arxiv created 2014/04/24 · arxiv updated 2014/04/28

Abstract

In this work we are going to study the dynamics of the linear automorphisms of a measure convolution algebra over a finite group, T(μ)=ν* μ. In order to understand an classify the asymptotic behavior of this dynamical system we provide an alternative to classical results, a very direct way to understand convergence of the sequence \νⁿ\_n∈ℕ, where G is a finite group, ν\inP(G) and νⁿ=\underbraceν∗...∗ν_n, trough the subgroup generated by his support.

Related

• Convolution semigroups for automorphism dynamics
• On the dynamics of a rational semigroup on a convolution measure algebra
• Comparing the automorphism group of the measure algebra with some groups related to the infinite permutation group of the natural numbers
• The automorphism group of a shift of linear growth: beyond transitivity
• The automorphism group of a minimal shift of stretched exponential growth