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 |
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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. |
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ISSN: | 0143-3857 1469-4417 |
DOI: | 10.1017/etds.2015.71 |