Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 31
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Sun, Taixiang and Xi, Hongjian 2016. The Centre and the Depth of the Centre for Continuous Maps on Dendrites with Finite Branch Points. Qualitative Theory of Dynamical Systems,


    Abdelrazak, Jmel 2015. Pointwise periodic homeomorphisms on dendrites. Dynamical Systems, Vol. 30, Issue. 1, p. 34.


    Wu, Xinxing and Chen, Guanrong 2014. Central limit theorem and chaoticity. Statistics & Probability Letters, Vol. 92, p. 137.


    Li, Risong 2013. The large deviations theorem and ergodic sensitivity. Communications in Nonlinear Science and Numerical Simulation, Vol. 18, Issue. 4, p. 819.


    Li, Risong 2012. A note on stronger forms of sensitivity for dynamical systems. Chaos, Solitons & Fractals, Vol. 45, Issue. 6, p. 753.


    Mai, Jiehua Zhang, Gengrong and Sun, Taixiang 2011. Recurrent points and non-wandering points of graph maps. Journal of Mathematical Analysis and Applications, Vol. 383, Issue. 2, p. 553.


    Sun, TaiXiang Xi, HongJian and Liang, HaiLan 2011. Special α-limit points and unilateral γ-limit points for graph maps. Science China Mathematics, Vol. 54, Issue. 9, p. 2013.


    Sun, Taixiang Su, Guangwang Liang, Hailan and He, Qiuli 2011. Topological Entropy and Specialα-Limit Points of Graph Maps. Discrete Dynamics in Nature and Society, Vol. 2011, p. 1.


    BALIBREA, F. CARABALLO, T. KLOEDEN, P. E. and VALERO, J. 2010. RECENT DEVELOPMENTS IN DYNAMICAL SYSTEMS: THREE PERSPECTIVES. International Journal of Bifurcation and Chaos, Vol. 20, Issue. 09, p. 2591.


    Mai, Jie-Hua and Shao, Song 2009. <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mover accent="true"><mml:mi>R</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mi>R</mml:mi><mml:mo>∪</mml:mo><mml:mover accent="true"><mml:mi>P</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> for graph maps. Journal of Mathematical Analysis and Applications, Vol. 350, Issue. 1, p. 9.


    Sun, Taixiang Xi, Hongjian and Chen, Zhanhuo 2008. On topological entropy of commuting tree maps. Nonlinear Analysis: Theory, Methods & Applications, Vol. 69, Issue. 1, p. 167.


    Sun, Taixiang 2008. On -limit sets of non-autonomous discrete systems on trees. Nonlinear Analysis: Theory, Methods & Applications, Vol. 68, Issue. 4, p. 781.


    Mai, Jie-hua and Sun, Tai-xiang 2007. Non-wandering points and the depth for graph maps. Science in China Series A: Mathematics, Vol. 50, Issue. 12, p. 1818.


    Hladký, Jan Novák, Jan Pyrih, Pavel Sterzik, Marek and Tancer, Martin 2006. An engine breaking the ΩEP-property. Topology and its Applications, Vol. 153, Issue. 18, p. 3621.


    Sun, Taixiang Xie, Mingde and Zhao, Jinfeng 2006. Equivalent conditions of a tree map with zero topological entropy. Bulletin of the Australian Mathematical Society, Vol. 73, Issue. 03, p. 321.


    Charatonik, Janusz J. 2005. On λ-Dendroids with the ΩEP-Property. Journal of Dynamical Systems and Geometric Theories, Vol. 3, Issue. 1, p. 55.


    Efremova, L. S. and Makhrova, E. N. 2005. On piecewise-monotone mappings with closed set of periodic points on dendrites. Journal of Mathematical Sciences, Vol. 126, Issue. 5, p. 1419.


    Efremova, L. S. and Makhrova, E. N. 2005. On piecewise-monotone mappings with closed set of periodic points on dendrites. Journal of Mathematical Sciences, Vol. 126, Issue. 5, p. 1419.


    Makarov, A. A. and Simonova, G. I. 2005. Problems of robust estimation in statistical models of daily traffic flow In the main channels of computer networks. Journal of Mathematical Sciences, Vol. 126, Issue. 1, p. 1024.


    Cánovas, José S. and Hric, Roman 2004. Distributional chaos of tree maps. Topology and its Applications, Vol. 137, Issue. 1-3, p. 75.


    ×
  • Bulletin of the Australian Mathematical Society, Volume 48, Issue 2
  • October 1993, pp. 347-350

The centre and the depth of the centre of a tree map

  • Xiangdong Ye (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972700015768
  • Published online: 01 April 2009
Abstract

Let X be a tree and f be a continuous map from X into itself. Denote by P(f) and R(f) the set of periodic points and the set of recurrent points of f respectively. We show in this note that the centre is and the depth of the centre is at most 3. Furthermore we have .

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      The centre and the depth of the centre of a tree map
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      The centre and the depth of the centre of a tree map
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      The centre and the depth of the centre of a tree map
      Available formats
      ×
Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax