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Homoclinic points of non-expansive automorphisms
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
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
Abstract [en]

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.
Keyword [en]
Homoclinic points, non-expansive automorphism, adjoint automorphism, entropy rank one action, common homoclinic points
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-36336DOI: 10.1007/s00010-007-2919-1ISI: 000207629900001Scopus ID: 2-s2.0-47949120249OAI: oai:DiVA.org:kth-36336DiVA: diva2:430620
Note
QC 20110711Available from: 2011-07-11 Created: 2011-07-11 Last updated: 2017-12-11Bibliographically approved

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