×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.