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Articles

Remarks on minimal sets on dendrites and finite graphs

Pages 1313-1322 | Received 01 Nov 2022, Accepted 25 May 2023, Published online: 05 Jun 2023

References

  • D. Arévalo, W.J. Charatonic, P.P. Covarrubias, and L. Simón, Dendrites with a closed set of end points, Topol. Appl. 115 (2001), pp. 1–17.
  • F. Balibrea, R. Hric, and L'. Snoha, Minimal sets on graphs and dendrites, Int. J. Bifurcat. Chaos Appl. Sci. Eng. 13 (2003), pp. 1721–1725.
  • F. Balibrea, T. Downarowicz, R. Hric, Ľ. Snoha, and V. S̆pitalský, Almost totally disconnected minimal systems, Ergod. Theory Dyn. Syst. 29 (2009), pp. 737–766.
  • J. Banks, Regular periodic decompositions for topologically transitive maps, Ergod. Theory Dyn. Syst.17 (1997), pp. 505–529.
  • Yu.S. Barkovskii and G.M. Levin, A Cantor limit set, Russ. Math. Surv. 35 (1980), pp. 235–236.
  • G.D. Birkhoff, Dynamical Systems, Amer. Math. Soc. Colloq. Publ., Vol. 9, American Mathematical Society, New York, 1927.
  • A. Blokh and E. Teoh, How little is little enough, Discrete Contin. Dyn. Syst. 9 (2003), pp. 969–978.
  • L. Block and J. Keesling, A characterization of adding machine maps, Topol. Appl. 140 (2004), pp. 151–161.
  • J. Charatonik and W. Charatonik, Dendrites, Aportaciones Mat. Comun. 22 (1998), pp. 227–253.
  • L.S. Efremova and E.N. Makhrova, The dynamics of monotone maps of dendrites, Matem. Sb. 192 (2001), pp. 15–30.
  • L.S. Efremova and E.N. Makhrova, One-dimensional dynamical systems, Russ. Math. Surv. 76 (2021), pp. 821–881.
  • M. Feigenbaum, Universal behavior in nonlinear systems, Los Alamos Sci. 1 (1980), pp. 4–27.
  • H.M. Gehman, Concerning the subsets of a plane continuous curve, Ann. Math. Second Series 27 (1925), pp. 29–46.
  • Z. Kočan, V. Kornecká-Kurková, and M. Málek, Entropy, horseshoes and homoclinic trajectories on trees, graphs and dendrites, Ergod. Theory Dyn. Syst. 31 (2011), pp. 165–175.
  • S. Kolyada and Ľ. Snoha, Minimal dynamical systems, Scholarpedia 4 (2009), p. 5803. https://www.scholarpedia.org/article/Minimal_dynamical_systems
  • K. Kuratowski, Topology, Academic Press, New York; PWN, Warsaw, Vol. 2, 1968.
  • J.-H. Mai, Pointwise-recurrent graph maps, Ergod. Theory Dyn. Syst. 25 (2005), pp. 629–637.
  • E.N. Makhrova, The structure of dendrites with the periodic point property, Russ. Math. (Iz. VUZ).55 (2011), pp. 33–37.
  • E.N. Makhrova, Structure of dendrites admitting an existence of arc horseshoe, Russ. Math. (Iz. VUZ) 59 (2015), pp. 52–61.
  • S. Nadler, Continuum Theory, Marcel Dekker, New York, 1992.
  • J. Nikiel, A characterization of dendroids with uncountable many end-points in the classical sense, Houst. J. Math. 9 (1983), pp. 421–432.
  • A.N. Sharkovsky, Yu.L. Maistrenko, and E.Yu. Romanenko, Difference Equations and Their Applications, Naukova Dumka, Kiev, Ukraine, 1986.
  • P. Urysohn, Über die Mächtigkeit der zusammenhängenden Mengen, Math. Ann. 94 (1925), pp. 262–295.
  • X. Ye, D-function of a minimal set and an extension of Sharkovskiĭ's theorem to minimal sets, Ergod. Theory Dyn. Syst. 12 (1992), pp. 365–376.

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