Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The space of invariant measures for countable Markov shifts   It is well known that the space of invariant probability measures for
transitive sub-shifts of finite type is a Poulsen simplex. In this article we
prove that in the non-compact setting, for a large family of transitive
countable Markov shifts, the space of invariant sub-probability measures is a
Poulsen simplex and that its extreme points are the ergodic invariant
probability measures together with the zero measure. In particular we obtain
that the space of invariant probability measures is a Poulsen simplex minus a
vertex and the corresponding convex combinations. Our results apply to finite
entropy non-locally compact transitive countable Markov shifts and to every
locally compact transitive countable Markov shift. In order to prove these
results we introduce a topology on the space of measures that generalizes the
vague topology to a class of non-locally compact spaces, the topology of
convergence on cylinders. We also prove analogous results for suspension flows
defined over countable Markov shifts.

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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc