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Mat. Sb., 2001, Volume 192, Number 6, Pages 15–30 (Mi msb570)  

This article is cited in 28 scientific papers (total in 28 papers)

The dynamics of monotone maps of dendrites

L. S. Efremova, E. N. Makhrova

N. I. Lobachevski State University of Nizhni Novgorod

Abstract: Monotone maps of dendrites with a countable closed set of branch points of finite order are studied. The structure of $\omega$-limit sets and of periodic and non-wandering sets is established, and it is proved that the topological entropy of monotone maps is equal to zero. It is shown that monotone maps of dendrites with a non-closed set of branch points of finite order may have properties different from those of the maps considered here.


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English version:
Sbornik: Mathematics, 2001, 192:6, 807–821

Bibliographic databases:

UDC: 517.9
MSC: Primary 37E25; Secondary 37B45, 54H20, 37B40
Received: 21.10.1999 and 25.12.2000

Citation: L. S. Efremova, E. N. Makhrova, “The dynamics of monotone maps of dendrites”, Mat. Sb., 192:6 (2001), 15–30; Sb. Math., 192:6 (2001), 807–821

Citation in format AMSBIB
\by L.~S.~Efremova, E.~N.~Makhrova
\paper The dynamics of monotone maps of dendrites
\jour Mat. Sb.
\yr 2001
\vol 192
\issue 6
\pages 15--30
\jour Sb. Math.
\yr 2001
\vol 192
\issue 6
\pages 807--821

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    This publication is cited in the following articles:
    1. Su G., Qin B., “Equicontinuous Dendrite Flows”, J. Differ. Equ. Appl.  crossref  mathscinet  isi
    2. Efremova L.S., Makhrova E.N., “On the center of continuous maps of dendrites”, J. Difference Equ. Appl., 9:3-4 (2003), 381–392  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. Chinen N., “Sets of all $\omega$-limit points for one-dimensional maps”, Houston J. Math., 30:4 (2004), 1055–1068  mathscinet  zmath  isi
    4. Kato H., “Topological entropy of monotone maps and confluent maps on regular curves”, Topology Proceedings, 28, no. 2, 2004, 587–593  mathscinet  zmath  isi
    5. Kato H., “Topological entropy of piecewise embedding maps on regular curves”, Ergodic Theory Dynam. Systems, 26:4 (2006), 1115–1125  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    6. Kato H., “Topological entropy of maps on regular curves”, Topology Appl., 154:6 (2007), 1027–1031  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    7. Mai Jiehua, Shi Enhui, “$\overline R=\overline P$ for maps of dendrites $X$ with $\mathrm{Card}(\mathrm{End}(X))<c$”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 19:4 (2009), 1391–1396  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    8. Acosta G., Illanes A., Méndez-Lango H., “The transitivity of induced maps”, Topology Appl., 156:5 (2009), 1013–1033  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. Wang Suhua, Shi Enhui, Zhou Lizhen, Su Xunli, “Topological transitivity and chaos of group actions on dendrites”, Int. J. Bifurcation Chaos Appl. Sci. Eng., 19:12 (2009), 4165–4174  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    10. Issam Naghmouchi, “Dynamical properties of monotone dendrite maps”, Topology and its Applications, 2011  crossref  mathscinet  isi  scopus  scopus  scopus
    11. E. N. Makhrova, “The structure of dendrites with the periodic point property”, Russian Math. (Iz. VUZ), 55:11 (2011), 33–37  mathnet  crossref  mathscinet
    12. Naghmouchi I., “Dynamics of Monotone Graph, Dendrite and Dendroid Maps”, Internat J Bifur Chaos Appl Sci Engrg, 21:11 (2011), 3205–3215  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    13. ISSAM NAGHMOUCHI, “Pointwise-recurrent dendrite maps”, Ergod. Th. Dynam. Sys, 2012, 1  crossref  mathscinet  isi  scopus  scopus  scopus
    14. SUHUA WANG, ENHUI SHI, YUJUN ZHU, BIN CHEN, “AUSLANDER–YORKE CHAOS FOR GROUP ACTIONS ON DENDRITES”, Int. J. Bifurcation Chaos, 23:06 (2013), 1350097  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    15. Taixiang Sun, Qiuli He, Hongjian Xi, “Intra-orbit separation of dense orbits of dendrite maps”, Chaos, Solitons & Fractals, 57 (2013), 89  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    16. Taixiang Sun, Qiuli He, Dongwei Su, Hongjian Xi, “Dendrite maps whose every periodic point is a fixed point”, Chaos, Solitons & Fractals, 65 (2014), 62  crossref  mathscinet  zmath  scopus  scopus  scopus
    17. Taixiang Sun, Zhanhe Chen, Xinhe Liu, Hongjian Xi, “Equicontinuity of dendrite maps”, Chaos, Solitons & Fractals, 69 (2014), 10  crossref  mathscinet  zmath  scopus  scopus  scopus
    18. Taixiang Sun, Qiuli He, Jing Liu, Chunyan Tao, Hongjian Xi, “Non-wandering Sets for Dendrite Maps”, Qual. Theory Dyn. Syst, 2014  crossref  mathscinet  scopus  scopus  scopus
    19. Taixiang Sun, Chunyan Tao, Hongjian Xi, Bin Qin, “Topological Limits andω-Limit Sets of the Dendrite Maps”, Journal of Dynamical Systems and Geometric Theories, 12:2 (2014), 165  crossref  mathscinet
    20. E. N. Makhrova, “Structure of dendrites admitting an existence of arc horseshoe”, Russian Math. (Iz. VUZ), 59:8 (2015), 52–61  mathnet  crossref
    21. Makhrova E.N., Vaniukova K.S., “On the set of non-wandering points of monotone maps on local dendrites”, Noma15 International Workshop on Nonlinear Maps and Applications, Journal of Physics Conference Series, 692, eds. Gelfreich V., FournierPrunaret D., LopezRuiz R., Callegari S., Nishio Y., Blokhina E., IOP Publishing Ltd, 2016, 012012  crossref  mathscinet  isi  scopus
    22. Marzougui H., Naghmouchi I., “Minimal sets for group actions on dendrites”, Proc. Amer. Math. Soc., 144:10 (2016), 4413–4425  crossref  mathscinet  zmath  isi  scopus
    23. Sun T.X., Su G.W., Xi H.J., Kong X., “Equicontinuity of Maps on a Dendrite With Finite Branch Points”, Acta. Math. Sin.-English Ser., 33:8 (2017), 1125–1130  crossref  mathscinet  zmath  isi  scopus
    24. Sun T., Tang Ya., Su G., Xi H., Qin B., “Special Alpha-Limit Points and Gamma-Limit Points of a Dendrite Map”, Qual. Theor. Dyn. Syst., 17:1 (2018), 245–257  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    25. Makhrova E., “On Strong Sensitive Points of Continuous Maps on Dendrites”, European Conference - Workshop Nonlinear Maps and Applications, Journal of Physics Conference Series, 990, IOP Publishing Ltd, 2018, UNSP 012006  crossref  mathscinet  isi  scopus  scopus  scopus
    26. Abdelli H., Abouda H., Marzougui H., “Nonwandering Points of Monotone Local Dendrite Maps Revisited”, Topology Appl., 250 (2018), 61–73  crossref  mathscinet  zmath  isi  scopus
    27. Sun T., Su G., Qin B., “The Depths of the Centres and the Attracting Centres of a Class of Dendrite Maps”, J. Math. Anal. Appl., 479:1 (2019), 1158–1171  crossref  mathscinet  zmath  isi
    28. Marzougui H., Naghmouchi I., “Minimal Sets and Orbit Spaces For Group Actions on Local Dendrites”, Math. Z., 293:3-4 (2019), 1057–1070  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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