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Limit periodic functions, adding machines, and solenoids

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Abstract

We prove that a stable adding machine invariant set for a homeomorphism of the plane is the limit of periodic points and also that a stable solenoid minimal invariant set for a three dimensional flow is the limit of periodic orbits. We give an example to show that a similar result is false in higher dimensions.

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Authors and Affiliations

  1. University of Cincinnati, 45221-0025, Cincinnati, Ohio

    Harold Bell & Kenneth R. Meyer

Authors
  1. Harold Bell
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  2. Kenneth R. Meyer
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This research partially supported by grants from the National Science Foundation and the Taft Foundation.

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Bell, H., Meyer, K.R. Limit periodic functions, adding machines, and solenoids. J Dyn Diff Equat 7, 409–422 (1995). https://doi.org/10.1007/BF02219369

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  • DOI: https://doi.org/10.1007/BF02219369

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