Homoclinic points of non-expansive automorphisms
2008 (English)In: Aequationes Mathematicae, ISSN 0001-9054, E-ISSN 1420-8903, Vol. 76, no 1-2, 1-18 p.Article in journal (Refereed) Published
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 every element of such an action has finite entropy, there can be no non-trivial common homoclinic points, unless the action is generated by a single automorphism.
Place, publisher, year, edition, pages
2008. Vol. 76, no 1-2, 1-18 p.
Homoclinic points, non-expansive automorphism, adjoint automorphism, entropy rank one action, common homoclinic points
IdentifiersURN: urn:nbn:se:kth:diva-36336DOI: 10.1007/s00010-007-2919-1ISI: 000207629900001ScopusID: 2-s2.0-47949120249OAI: oai:DiVA.org:kth-36336DiVA: diva2:430620
QC 201107112011-07-112011-07-112011-07-11Bibliographically approved