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A note on the dynamics of cyclically permuted direct product maps. (English) Zbl 1337.54031
This paper studies the topological dynamics of maps of the form $$(x_1,\dots,x_n)\mapsto(f_{\tau(1)}(x_{\tau{1}}),\dots, f_{\tau(n)}(x_{\tau(n)}))$$ on $$X_1\times\cdots\times X_n$$, the maps $$f_{\tau(i)}:X_{\tau(i)}\to X_i$$ are continuous and $$\tau$$ is a cyclic permutation of $$\{1,\dots,n\}$$. Topological transitivity and weak topological mixing are related to an iterated function system defined by the map.

##### MSC:
 54H20 Topological dynamics (MSC2010) 37E99 Low-dimensional dynamical systems
##### Keywords:
topological dynamics; cyclic permutation maps
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##### References:
 [1] Balibrea, F.; Cánovas, J. S.; Linero, A., On ω-limit sets of antitriangular maps, Topol. Appl., 137, 13-19, (2004) · Zbl 1042.54026 [2] Balibrea, F.; Linero, A., Periodic structure of σ-permutation maps on $$I^n$$, Aequ. Math., 62, 265-279, (2001) · Zbl 0991.37016 [3] Banks, J., Regular periodic decompositions for topologically transitive maps, Ergod. Theory Dyn. Syst., 17, 505-529, (1997) · Zbl 0921.54029 [4] Bischi, G. I.; Mammana, C.; Gardini, L., Multistability and cyclic attractors in duopoly games, Chaos Solitons Fractals, 11, 543-564, (2000) · Zbl 0960.91017 [5] Block, L.; Coppel, W. A., Dynamics in one dimension, Lect. Notes Math., vol. 1513, (1992), Springer-Verlag Berlin [6] Dana, R. A.; Montrucchio, L., Dynamical complexity in duopoly games, J. Econ. Theory, 40, 40-56, (1986) · Zbl 0617.90104 [7] Franke, J. E.; Yakubu, A.-A., Attenuant cycles in periodically forced discrete-time age-structured population models, J. Math. Anal. Appl., 316, 69-86, (2006) · Zbl 1083.92037 [8] Furstenberg, H., Disjointness in ergodic theory, minimal sets and a problem in Diophantine approximation, Math. Syst. Theory, 1, 1-49, (1967) · Zbl 0146.28502 [9] Kolyada, S.; Snoha, L’., Some aspects of topological transitivity - a survey, Grazer Math. Ber., 334, 3-35, (1997) · Zbl 0907.54036 [10] Puu, T., Nonlinear economic dynamics, (1997), Springer Berlin · Zbl 0931.91024
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