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).
Mike Boyle (2017-07-27 16:33:30 -0700 -0700):
The ergodic nonhyperbolic toral automorphisms do not admit covers by shifts of
finite type, but there are other symbolic representations. See
[LindenstraussSchmidt2005]
.
Douglas Lind (2017-07-29 07:34:00 -0700 -0700):
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
[SchmidtToral]
.
Douglas Lind (2017-07-30 08:00:46 -0700 -0700):
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.
Comments
Not really; cf [lind1982dynamical]
See also [marcus1980periodic] .
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 toral automorphisms do not admit covers by shifts of finite type, but there are other symbolic representations. See [LindenstraussSchmidt2005] .
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 [SchmidtToral] .
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.