Summary.
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.
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Manuscript received: August 17, 2006 and, in final form, April 17, 2007.
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Miles, R. Homoclinic points of non-expansive automorphisms. Aequ. math. 76, 1–18 (2008). https://doi.org/10.1007/s00010-007-2919-1
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DOI: https://doi.org/10.1007/s00010-007-2919-1