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Franco Barragán
franco@mixteco.utm.mx
Franco Barragán
Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, Carretera a Acatlima, Km. 2.5, Huajuapan de León, Oaxaca, C.P. 69000, México
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Sergio Macías
sergiom@matem.unam.mx
Sergio Macías
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, Ciudad de México, CDMX, C.P. 04510, México
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Anahí Rojas
anacarrasco.rr@gmail.com
Anahí Rojas
Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, Carretera a Acatlima, Km. 2.5, Huajuapan de León, Oaxaca, C.P. 69000, México
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Let X be a topological space. For any positive integer n, we consider the n-fold symmetric product of X, ℱn(X), consisting of all nonempty subsets of X with at most n points; and for a given function ƒ : X → X, we consider the induced functions ℱn(ƒ): ℱn(X) → ℱn(X). Let M be one of the following classes of functions: exact, transitive, ℤ-transitive, ℤ+-transitive, mixing, weakly mixing, chaotic, turbulent, strongly transitive, totally transitive, orbit-transitive, strictly orbit-transitive, ω-transitive, minimal, I N, T T++, semi-open and irreducible. In this paper we study the relationship between the following statements: ƒ ∈ M and ℱn(ƒ) ∈ M.
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-
[1]
Akin, E. The General Topology of Dynamical Systems, vol. 1. American Mathematical Society, Providence, 1993.
-
[2]
Akin, E., and Carlson, J. Conceptions of topological transitivity. Topology and its Applications 159 (2012), 2815–2830. doi:.
-
[3]
Auslander, J., Greschonig, G., and Nagar, A. Reflections on equicontinuity. Proceedings of the American Mathematical Society 142 (2014), 3129–3137. doi:.
-
[4]
Banks, J. Topological mapping properties defined by digraphs. Discrete&Continuous Dynamical Systems 5 (1999), 83–92. doi:.
-
[5]
Banks, J. Chaos for induced hyperspace maps. Chaos, Solitons & Fractals 25 (2005), 681–685.doi:.
-
[6]
Barragan, F., Macias, S., and Tenorio, J. More on induced maps on n-fold symmetric product suspensions. Glasnik Matematicki 50 (2015), 489–512. doi:.
-
[7]
Barragan, F., Santiago, A., and Tenorio, J. F. Dynamic properties for the induced maps on n-fold symmetric product suspensions. Glasnik Matematicki 51 (2016), 453–474. doi:.
-
[8]
Bauer, W., and Sigmund, K. Topological dynamics of transformations induced on the space of probability measures. Monatshefte für Mathematik 79 (1975), 81–92. doi:.
-
[9]
Bilokopytov, E., and Kolyada, S. Transitive maps on topological spaces. Ukrainian Mathematical Journal 65 (2014), 1293–1318. doi:.
-
[10]
Birkhoff, G. Dynamical Systems, vol. 9. American Mathematical Society, Providence, 1927.
-
[11]
Borsuk, K., and Ulam, S. On symmetric products of topological space. Bulletin of the American Mathematical Society 37 (1931), 875–882. doi:.
-
[12]
Brown, T., and Comfort, W. New method for expansion and contraction maps in uniform spaces. Proceedings of the American Mathematical Society 11 (1960), 483–486. doi:.
-
[13]
Bryant, B. On expansive homeomorphisms. Pacific Journal of Mathematics 10 (1960), 1163–1167.
-
[14]
Fernandez, L., Good, C., and M. Puljiz, Á. R. Chain transitivity in hyperspaces. Chaos, Solitons & Fractals 81 (2015), 83–90. doi:.
-
[15]
Furstenberg, H. Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation. Mathematical systems theory 1 (1967), 1–49. doi:.
-
[16]
Gomez, J., Illanes, A., and Mendez, H. Dynamic properties for the induced maps in the symmetric products. Chaos Solitons & Fractals 45 (2012), 1180–1187. doi:.
-
[17]
Good, C., and Macias, S. Symmetric products of generalized metric spaces. Topology and its Applications 206 (2016), 93–114. doi:.
-
[18]
Good, C., and Macias, S. What is topological about topological dynamics? Discrete & Continuous Dynamical Systems-A 38 (2018), 1007–1031. doi:.
-
[19]
Gotschalk, W., and Hedlun, G. Topological Dynamics, vol. 36. American Mathematical= Society, Providence, 1955.
-
[21]
Higuera, G., and Illanes, A. Induced mappings on symmetric products. Topology Proceedings 37 (2011), 367–401.
-
[22]
Hood, B. Topological entropy and uniform spaces. Journal of the London Mathematical Society 8 (1974), 633–641. doi:.
-
[23]
Illanes, A., and Jr, S. N. Hyperspaces: fundamentals and recent advances, vol. 216 of Monographs and Textbooks in Pure and Applied Math. Marcel Dekker, New York, Basel, 1999.
-
[24]
Jr, S. N. Hyperspaces of sets, vol. 49 of Monographs and Textbooks in Pure and Applied Math. Marcel Dekker, New York, Basel, 1978. Reprinter In: Aportaciones Matemáticas, Serie Textos No. 33, Sociedad Matemática Mexicana, 2006.
-
[25]
Kolyada, S.Snoha, L., and Trofimchuk, S. Noninvertible minimal maps. Fundamenta Mathematicae 168 (2001), 141–163. doi:.
-
[26]
Kwietniak, D., and Misiurewicz, M. Exact devaney chaos and entropy. Qualitative Theory of Dynamical Systems 6 (2005), 169–179. doi:.
-
[27]
Kwietniak, D., and Oprocha, P. Topological entropy and chaos for maps induced on hyperspaces. Chaos, Solitons & Fractals 33 (2007), 76–86. doi:.
-
[28]
Lampart, M., and Raith, P. Topological entropy for set valued maps. Nonlinear Analysis 73 (2010), 1533–1537. doi:.
-
[29]
Li, R. A note on stronger forms of sensitivity for dynamical systems. Chaos Solitons & Fractals 45 (2012), 753–758. doi:.
-
[30]
Liao, G., Wang, L., and Zhang, Y. Transitivity, mixing and chaos for a class of set-valued mappings. Science in China Series A 49 (2006), 1–8. doi:.
-
[31]
Macias, S. Aposyndetic properties of symmetric product of continua. Topology Proceedings 22 (1997), 281–296.
-
[32]
Macias, S. On symmetric product of continua. Topology and its Applications 92 (1999), 173–182. doi:.
-
[34]
Mai, J., and Sun, W. Transitivities of maps of general topological spaces. Topology and its Applications 157 (2010), 946–953. doi:.
-
[35]
Martinez-Montejano, J. Mutual aposyndesis of symmetric products. Topology Proceedings 24 (1999).
-
[36]
Michael, E. Topologies on spaces of subsets. Transactions of the American Mathematical Society 71 (1951), 152–182. doi:.
-
[37]
Pena, J., and Lopez, G. Topological entropy for induced hyperspace maps. Chaos Solitons & Fractals 28 (2006), 979–982. doi:.
-
[38]
Peng, L., and Sun, Y. A study of symmetric products of generalized metric spaces. Topology and its Applications 231 (2017), 411–429. doi:.
-
[39]
Peris, A. Set-valued discrete chaos. Chaos, Solitons & Fractals 26 (2005), 19–23. doi:.
-
[40]
Roman-Flores, H. A note on transitivity in set-valued discrete systems. Chaos Solitons & Fractals 17 (2003), 99–104. doi:.
-
[41]
Sabbaghan, M., and Damerchiloo, H. A note on periodic points and transitive maps. Mathematical Sciences 5 (2011), 259–266.
-
[42]
Tang, Z., Lin, S., and Lin, F. Symmetric products and closed finite-to-one mappings. Topology and its Applications 234 (2018), 26–45. doi:.
-
[43]
Vietoris, L. Bereiche zweiter ordnung. Monatshefte für Mathematik und Physik 32 (1922), 258–280. doi:.
-
[44]
Wang, Y., Wei, G., and Campbell, W. Sensitive dependence on initial conditions between dynamical systems and their induced hyperspace dynamical systems. Topology and its Applications 156 (2009), 803–811. doi:.
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