Self Duality and Codings for Expansive Group Automorphisms

The Adjoint Action of an Expansive Algebraic Z–Action

Let d ≥ 1, and let α be an expansive Z-action by continuous automorphisms of a compact abelian group X with completely positive entropy. Then the group ∆α(X) of homoclinic points of α is countable and dense in X, and the restriction of α to the α-invariant subgroup ∆α(X) is a Z-action by automorphisms of ∆α(X). By duality, there exists a Z-action α∗ by automorphisms of the compact abelian group...

Homoclinic points of non-expansive automorphisms

We study homoclinic points of non-expansive automorphisms of compact abelian groups. Connections between the existence of non-trivial homoclinic points, expansiveness, entropy and adjoint automorphisms (in the sense of Einsiedler and Schmidt) are explored. Some implications for countable abelian group actions by automorphisms of compact abelian groups are also considered and it is shown that if...

Bijective Arithmetic Codings of Hyperbolic Automorphisms of the 2-torus, and Binary Quadratic Forms

We study the arithmetic codings of hyperbolic automorphisms of the 2torus, i.e. the continuous mappings acting from a certain symbolic space of sequences with a finite alphabet endowed with an appropriate structure of additive group onto the torus which preserve this structure and turn the two-sided shift into a given automorphism of the torus. This group is uniquely defined by an automorphism,...

Modified Halpern Iteration of Asymptotically Non-Expansive Mappings

Finite automorphisms of negatively curved Poincaré Duality groups

In this paper, we show that if G is a finite p-group (p prime) acting by automorphisms on a δ-hyperbolic Poincaré Duality group over Z, then the fixed subgroup is a Poincaré Duality group over Zp. We also provide a family of examples to show that the fixed subgroup might not be a Poincaré Duality group over Z. In fact, the fixed subgroups in our examples even fail to be duality groups over Z.