698 research outputs found
Phase transitions for suspension flows
This paper is devoted to study thermodynamic formalism for suspension flows
defined over countable alphabets. We are mostly interested in the regularity
properties of the pressure function. We establish conditions for the pressure
function to be real analytic or to exhibit a phase transition. We also
construct an example of a potential for which the pressure has countably many
phase transitions.Comment: Example 5.2 expanded. Typos corrected. Section 6.1 superced the note
"Thermodynamic formalism for the positive geodesic flow on the modular
surface" arXiv:1009.462
Two-sided shift spaces over infinite alphabets
Ott, Tomforde, and Willis proposed a useful compactification for one-sided
shifts over infinite alphabets. Building from their idea we develop a notion of
two-sided shift spaces over infinite alphabets, with an eye towards
generalizing a result of Kitchens. As with the one-sided shifts over infinite
alphabets our shift spaces are compact Hausdorff spaces but, in contrast to the
one-sided setting, our shift map is continuous everywhere. We show that many of
the classical results from symbolic dynamics are still true for our two-sided
shift spaces. In particular, while for one-sided shifts the problem about
whether or not any -step shift is conjugate to an edge shift space is open,
for two-sided shifts we can give a positive answer for this question.Comment: 32 page
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