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Spaces of transitive interval maps. (English) Zbl 1352.37115

Summary: On a compact real interval, the spaces of all transitive maps, all piecewise monotone transitive maps and all piecewise linear transitive maps are considered with the uniform metric. It is proved that they are contractible and uniformly locally arcwise connected. Then the spaces of all piecewise monotone transitive maps with given number of pieces as well as various unions of such spaces are considered and their connectedness properties are studied.

MSC:

37E05 Dynamical systems involving maps of the interval
54H20 Topological dynamics (MSC2010)
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[1] DOI: 10.3792/pja/1195571228 · Zbl 0044.12503 · doi:10.3792/pja/1195571228
[2] Fathi, Ann. Sci. Éc. Norm. Supér. 4 13 pp 45– (1980)
[3] DOI: 10.1112/jlms/jdt073 · Zbl 1311.57046 · doi:10.1112/jlms/jdt073
[4] Dobrowolski, Proc. Amer. Math. Soc. 98 pp 303– (1986)
[5] DOI: 10.1142/4205 · doi:10.1142/4205
[6] DOI: 10.2969/jmsj/06130687 · Zbl 1176.28017 · doi:10.2969/jmsj/06130687
[7] Hocking, Topology (1988)
[8] DOI: 10.1090/S0002-9947-1966-0197683-5 · doi:10.1090/S0002-9947-1966-0197683-5
[9] DOI: 10.1090/S0002-9939-1990-1009997-6 · doi:10.1090/S0002-9939-1990-1009997-6
[10] Milnor, Dynamical Systems College Park, MD, 1986–87 pp 465– (1988)
[11] Kuratowski, Topology. Vol. II (1968)
[12] Kolyada, Scholarpedia 4 (2009)
[13] Keane, Proc. Amer. Math. Soc. 26 pp 420– (1970)
[14] Whyburn, Analytic Topology (1971)
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