Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group Colorings and Bernoulli Subflows   In this paper we study the dynamics of Bernoulli flows and their subflows
over general countable groups from the symbolic and topological perspectives.
We study free subflows (subflows in which every point has trivial stabilizer),
minimal subflows, disjointness of subflows, the problem of classifying subflows
up to topological conjugacy, and the differences in dynamical behavior between
pairs of points which disagree on finitely many coordinates. We call a point
hyper aperiodic if the closure of its orbit is a free subflow and we call it
minimal if the closure of its orbit is a minimal subflow.
  We prove that the set of all (minimal) hyper aperiodic points is always dense
but also meager and null. By employing notions and ideas from descriptive set
theory, we study the complexity of the sets of hyper aperiodic points and of
minimal points and completely determine their descriptive complexity. In doing
this we introduce a new notion of countable flecc groups and study their
properties. We obtain a dichotomy for the complexity of classifying free
subflows up to topological conjugacy. For locally finite groups the topological
conjugacy relation for all (free) subflows is hyperfinite and nonsmooth. For
nonlocally finite groups the relation is Borel bireducible with the universal
countable Borel equivalence relation.
  A primary focus of the paper is to develop constructive methods for the
notions studied. To construct hyper aperiodic points, a fundamental method of
construction of multi-layer marker structures is developed with great
generality. Variations of the fundamental method are used in many proofs in the
paper, and we expect them to be useful more broadly in geometric group theory.
As a special case of such marker structures, we study the notion of ccc groups
and prove the ccc-ness for countable nilpotent, polycyclic, residually finite,
locally finite groups and for free products.

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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: bayes-an