Fedeli, Alessandro On chaotic set-valued discrete dynamical systems. (English) Zbl 1079.37021 Chaos Solitons Fractals 23, No. 4, 1381-1384 (2005). The author shows some connections between the chaoticity of a discrete dynamical system and the chaoticity of several set-valued discrete dynamical systems associated to it. He indicates that this kind of investigation should be useful in the study of every phenomenon in which one wants to understand the relationships between the dynamics of individual movement and the dynamics of collective movements. Reviewer: Messoud A. Efendiev (Berlin) Cited in 1 ReviewCited in 33 Documents MSC: 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 39A99 Difference equations Keywords:discrete dynamical systems; chaoticity; set-valued systems PDF BibTeX XML Cite \textit{A. Fedeli}, Chaos Solitons Fractals 23, No. 4, 1381--1384 (2005; Zbl 1079.37021) Full Text: DOI References: [1] Alsedá, L.; Kolyada, S. F.; Llibre, J.; Saoha, L., Entropy and periodic points for transitive maps, Trans. Amer. Math. Soc., 351, 1551-1573 (1999) · Zbl 0913.58034 [2] Banks, J.; Brooks, J.; Cairns, G.; Stacey, P., On the Devaney’s definition of chaos, Amer. Math. Monthly, 99, 332-334 (1992) · Zbl 0758.58019 [3] Block, L. S.; Coppel, W. A., Dynamics in one dimension (1992), Springer-Verlag [4] Devaney, R. L., An introduction to chaotic dynamical systems (1989), Addison-Wesley · Zbl 0695.58002 [5] El Naschie, M. S., Chaos and fractals in nano and quantum technology, Chaos, Solitons & Fractals, 9, 1793-1802 (1998) · Zbl 0989.37520 [6] Engelking, R., General topology (1989), Heldermann Verlag · Zbl 0684.54001 [7] Knudsen, C., Chaos without nonperiodicity, Amer. Math. Monthly, 101, 563-565 (1994) · Zbl 0840.54031 [8] Román-Flores, H., A note on transitivity in set-valued discrete systems, Chaos, Solitons & Fractals, 17, 99-104 (2003) · Zbl 1098.37008 [9] Sharkovsky, A. N., Nonwandering points and the centre of a continuous mapping of the line into itself, Dopovidi Ukrain. Acad. Sci., 7, 865-868 (1964), [in Ukrainian] · Zbl 0173.25601 [10] Shi, Y.; Chen, G., Chaos of discrete dynamical systems in complete metric spaces, Chaos, Solitons & Fractals, 22, 555-571 (2004) · Zbl 1067.37047 [11] Silverman, S., On maps with dense orbits and the definition of chaos, Rocky Mountain J. Math., 22, 353-375 (1992) · Zbl 0758.58024 [12] Vellekoop, M.; Berglund, R., On intervals, Transitivity=Chaos, Amer. Math. Monthly, 101, 353-355 (1994) · Zbl 0886.58033 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.