Markov partitions and homology for -solenoids

Given a relatively prime pair of integers, $n\geq m>1$ , there is associated a topological dynamical system which we refer to as an $n/m$ -solenoid. It is also a Smale space, as defined by David Ruelle, meaning that it has local coordinates of contracting and expanding directions. In this case, t...

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Veröffentlicht in:Ergodic theory and dynamical systems 2017-05, Vol.37 (3), p.716-738
Hauptverfasser: BURKE, NIGEL D., PUTNAM, IAN F.
Format: Artikel
Sprache:eng
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Zusammenfassung:Given a relatively prime pair of integers, $n\geq m>1$ , there is associated a topological dynamical system which we refer to as an $n/m$ -solenoid. It is also a Smale space, as defined by David Ruelle, meaning that it has local coordinates of contracting and expanding directions. In this case, these are locally products of the real and various $p$ -adic numbers. In the special case, $m=2,n=3$ and for $n>3m$ , we construct Markov partitions for such systems. The second author has developed a homology theory for Smale spaces and we compute this in these examples, using the given Markov partitions, for all values of $n\geq m>1$ and relatively prime.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2015.71