Homoclinic points of non-expansive automorphisms

MILES, Richard (2008). Homoclinic points of non-expansive automorphisms. Aequationes Mathematicae, 26 (1-2), 1-18.

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Official URL: https://doi.org/10.1007/s00010-007-2919-1
Link to published version:: https://doi.org/10.1007/s00010-007-2919-1
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    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.

    Item Type: Article
    Departments - Does NOT include content added after October 2018: Faculty of Social Sciences and Humanities > Department of Teacher Education
    Identification Number: https://doi.org/10.1007/s00010-007-2919-1
    Page Range: 1-18
    Depositing User: Richard Miles
    Date Deposited: 26 Jan 2018 14:06
    Last Modified: 26 Jan 2018 14:06
    URI: http://shura.shu.ac.uk/id/eprint/17233

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