PermalinkSubmitted by Anthonyquas on Thu, 12/01/2016 - 22:09
Lemma 2.1 of this paper shows a specification-like property provided the gaps between specified blocks grow sub-linearly in the lengths of the orbit segments that are being constrained. (For ordinary specification, these gaps are of constant length).
PermalinkSubmitted by Douglas Lind on Sat, 07/29/2017 - 07:34
The state of the art in symbolic representations of toral automorphisms is contained in the paper *Representations of toral automorphisms* by Klaus Schmidt, Topology and its applications 205 (2016), 88-116 [1] .
PermalinkSubmitted by Douglas Lind on Sun, 07/30/2017 - 08:00
A complete description of the specification properties of ergodic toral automorphisms is given in "Ergodic group automorphisms and specification", Douglas Lind, Springer Lecture Notes in Mathematics 729 (1978), 93-104. Toral automorphisms come in three flavors, depending on the behavior on the generalized eigenspace for eigenvalues of modulus one (if any), and the specification behavior is different for each flavor.
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Comments
FL
Not really; cf [1]
References
BHM
See also [1].
References
Lemma 2.1 of this paper shows
Lemma 2.1 of this paper shows a specification-like property provided the gaps between specified blocks grow sub-linearly in the lengths of the orbit segments that are being constrained. (For ordinary specification, these gaps are of constant length).
The ergodic nonhyperbolic
The ergodic nonhyperbolic toral automorphisms do not admit covers by shifts of finite type, but there are other symbolic representations. See [1].
References
The state of the art in
The state of the art in symbolic representations of toral automorphisms is contained in the paper *Representations of toral automorphisms* by Klaus Schmidt, Topology and its applications 205 (2016), 88-116 [1] .
References
A complete description of the
A complete description of the specification properties of ergodic toral automorphisms is given in "Ergodic group automorphisms and specification", Douglas Lind, Springer Lecture Notes in Mathematics 729 (1978), 93-104. Toral automorphisms come in three flavors, depending on the behavior on the generalized eigenspace for eigenvalues of modulus one (if any), and the specification behavior is different for each flavor.
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