Liapunov Stability and the ring of P-adic integers
It is well-known that stable Cantor sets are topologically conjugate to adding machines. In this work we show are also conjugate to an algebraic object, the ring ofP−adic integers with respect to group tramnslation. This ring is closely related to the field of p-adic numbers; connections and distintions are explored. The inverse limit construction provides a purely dynamical proof of an algebraic result: the classification of adding machines, or P−adic integers, up to group isomorphism.
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Buescu, J. (2008). Liapunov Stability and the ring of P-adic integers. São Paulo Journal of Mathematical Sciences, 2(1), 78-83. https://doi.org/10.11606/issn.2316-9028.v2i1p78-83