Strongly Mixing Transformations and Geometric Diameters - Fatkić, Huse; Brkić, Mehmed (Sarajevo Journal of Mathematics, 2024)
In this paper, we investigate metric properties and dispersive effects of strongly mixing transformations on general metric spaces endowed with a finite measure; in particular, we investigate their connections with the theory of generalized (geometric) diameters on general metric spaces. We first show that the known result by Rice [17,Theorem 2] (motivated by some physical phenomena and offer some clarifications of these phenomena), which is a substantial improvement of Theorems 1 and 2 due to Erber, Schweizer and Sklar [4], can be generalized in such a way that this result remains valid when ``ordinary diameter" is replaced by ``geometric diameter of any finite order". Next we show that ``ordinary essential diameter" in the mentioned Rice's result can be replaced by ``essential geometric diameter of any finite order". These results also complement the previous results of Fatkić , Saff and Sempi. 2000 Mathematics Subject Classification. 37A25, 26A18, 28A10