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On pressure of dynamical systems induced by probability bi-sequences | ||
| Journal of Finsler Geometry and its Applications | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 خرداد 1405 اصل مقاله (355.42 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2026.19659.1208 | ||
| نویسندگان | ||
| Mehdi Rahimi* ؛ Asghar Ghodrati | ||
| Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran | ||
| چکیده | ||
| In this paper, we introduce a new family of metrics on topological dynamical systems, induced by probability bi-sequences, which generalizes both the classical Bowen metric and the mean metric. Using these metrics, we define measure-theoretic and topological pressure and show that these quantities coincide with the classical topological pressure and the sum of measure-theoretic entropy and integral of the potential function, respectively. The results hold under the following mild condition on the probability bi-sequence Γ ={γm,n}m,n≥ 0: limsupn→∞ [(γn*)-1/n] < ∞, where γn* := min0≤ i ≤ nγi,n. This condition is satisfied for a broad class of bi-sequences, including the uniform weights γm,n = 1/(n+1) that recover the mean metric case. As an application, we extend the pressure versions of Katok's entropy formula to this more general setting. Our work unifies and generalizes several previous results on pressure in mean metrics. | ||
| کلیدواژهها | ||
| Katok's entropy formula؛ measure-theoretic pressure؛ probability bi-sequence | ||
| مراجع | ||
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