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A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-sided continuous function
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Walters, Peter (2003) A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-sided continuous function. Dynamical Systems, Vol.18 (No.2). pp. 131-138. doi:10.1080/1468936031000095672 ISSN 1468-9367.
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Official URL: http://dx.doi.org/10.1080/1468936031000095672
Abstract
If (T) over cap:(X) over cap -->(X) over cap is a two-sided subshift on a finite number of symbols and T:X-->X is the corresponding one-sided subshift we give a necessary and sufficient condition for a continuous function (f) over cap:(X) over cap -->(R) over cap to be cohomologous, with respect to ((X) over cap(T) over cap), to a continuous function which can be defined on X. The property of being cohomologous to such a 'one-sided' function is important in the study of equilibrium states because there are extra tools, such as the Ruelle transfer operator, for one-sided systems. We present the results in the more general context when T : X-->X is a continuous surjection of a compact metric space and (T) over cap:(X) over cap -->(X) over cap is its natural extension, and look at the special case of subshifts. We also prove some related results and give applications to subshifts.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Dynamical Systems | ||||
Publisher: | Taylor & Francis Ltd. | ||||
ISSN: | 1468-9367 | ||||
Official Date: | June 2003 | ||||
Dates: |
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Volume: | Vol.18 | ||||
Number: | No.2 | ||||
Number of Pages: | 8 | ||||
Page Range: | pp. 131-138 | ||||
DOI: | 10.1080/1468936031000095672 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Description: | This article was removed from online journal because of errors in the paper. |
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