Markov partitions and homology for -solenoids
2015 ◽
Vol 37
(3)
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pp. 716-738
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Keyword(s):
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.
2013 ◽
Vol 34
(6)
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pp. 2066-2092
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Keyword(s):
2012 ◽
Vol 32
(4)
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pp. 1370-1399
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Keyword(s):
2006 ◽
Vol 16
(05)
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pp. 849-874
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Keyword(s):
Keyword(s):
1979 ◽
Vol 85
(3)
◽
pp. 477-491
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Keyword(s):
2020 ◽
Vol 0
(0)
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2018 ◽
Vol 40
(4)
◽
pp. 953-974
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