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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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