TY  - JOUR
T1  - Dispersion Under Iteration of Strongly Mixing Transformations on Metric Spaces
TT  - Original Research Paper
AU  - Fatkić, Hana
AU  - Sklar, Abe
AU  - Fatkić, Huse
PY  - 2015
DA  - June
DO  - 10.18100/ijamec.90047
JF  - International Journal of Applied Mathematics Electronics and Computers
PB  - PLUSBASE AKADEMİ ORGANİZASYON VE DANIŞMANLIK
WT  - DergiPark
SN  - 2147-8228
SP  - 150
EP  - 154
VL  - 3
IS  - 3
LA  - en
AB  - In this paper, we investigate metric properties and dispersive effects of strongly mixing transformations on general metric spaces endowed with a probability measure; in particular, we investigate their connections with the theory of generalized (α-harmonic) diameters on general metric spaces. We first show that the known result by R. E. Rice ([Aequationes Math. 17(1978), 104-108], 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 T. Erber, B. Schweizer and A. Sklar [Comm. Math. Phys., 29 (1973), 311 – 317], can be generalized in such a way that this result remains valid when "ordinary diameter" is replaced by "α-harmonic diameter of any finite order". Next we show that "ordinary essential diameter" in the mentioned Rice's result can be replaced by the" essential α-harmonic diameter of any finite order". These results also complement the previous results (on dynamical systems with discrete time and/or generalised diameters) of N. Faried and M. Fathey, H. Fatkić, E. B. Saff, S. Sekulović and V. Zakharyuta.
KW  - Dispersion under iteration
KW  - diameter
KW  - harmonic n-diameter
KW  - measurability-preserving dynamical systems
KW  - measure
KW  - metric space
KW  - mixing transformations
KW  - probability space.
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UR  - https://doi.org/10.18100/ijamec.90047
L1  - https://dergipark.org.tr/en/download/article-file/89461
ER  -