Shadowing in actions of some Abelian groups
We study shadowing properties of continuous actions of the groups and . Necessary and sufficient conditions are given under which a linear action of on has a Lipschitz shadowing property.
We study shadowing properties of continuous actions of the groups and . Necessary and sufficient conditions are given under which a linear action of on has a Lipschitz shadowing property.
Denote by , , the regular tree whose vertices have valence , its boundary. Yu. A. Neretin has proposed a group of transformations of , thought of as a combinatorial analogue of the diffeomorphism group of the circle. We show that is generated by two groups: the group of tree automorphisms, and a Higman-Thompson group . We prove the simplicity of and of a family of its subgroups.