Garden of Eden and specification
2018 ◽
Vol 39
(11)
◽
pp. 3075-3088
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Keyword(s):
We establish a Garden of Eden theorem for expansive algebraic actions of amenable groups with the weak specification property, i.e. for any continuous equivariant map $T$ from the underlying space to itself, $T$ is pre-injective if and only if it is surjective. In particular, this applies to all expansive principal algebraic actions of amenable groups and expansive algebraic actions of $\mathbb{Z}^{d}$ with completely positive entropy.
2008 ◽
Vol 28
(1)
◽
pp. 87-124
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2002 ◽
Vol 196
(1)
◽
pp. 1-18
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2014 ◽
Vol 367
(12)
◽
pp. 8579-8595
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1998 ◽
Vol 18
(4)
◽
pp. 859-874
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Keyword(s):
2009 ◽
Vol 15
(1)
◽
pp. 87-95
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2014 ◽
Vol 202
(1)
◽
pp. 461-474
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2013 ◽
Vol 34
(6)
◽
pp. 2054-2065
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2011 ◽
Vol 32
(3)
◽
pp. 919-940
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Keyword(s):