A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-sided continuous function
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. ISSN 1468-9367Full text not available from this repository.
Official URL: http://dx.doi.org/10.1080/1468936031000095672
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|
|Subjects:||Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Dynamical Systems|
|Publisher:||Taylor & Francis Ltd.|
|Official Date:||June 2003|
|Number of Pages:||8|
|Page Range:||pp. 131-138|
This article was removed from online journal because of errors in the paper.
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