Simple dynamical systems

• Ali Akbar, K. ^[1] ; Kannan, V. ^[2] ; Subramania Pillai, I. ^[3]
  1. [1] Central University of Kerala

     Central University of Kerala

     India

     
  2. [2] University of Hyderabad

     University of Hyderabad

     India

     
  3. [3] Pondicherry University

     Pondicherry University

     India

     

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 20, Nº. 2, 2019, págs. 307-324
• Idioma: inglés
• DOI: 10.4995/agt.2019.7910
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• Resumen

  • In this paper, we study the class of simple systems on R induced by homeomorphisms having finitely many non-ordinary points. We characterize the family of homeomorphisms on R having finitely many non-ordinary points upto (order) conjugacy. For x,y ∈ R, we say x ∼ y on a dynamical system (R,f) if x and y have same dynamical properties, which is an equivalence relation. Said precisely, x ∼ y if there exists an increasing homeomorphism h : R → R such that h ◦ f = f ◦ h and h(x) = y. An element x ∈ R is ordinary in (R,f) if its equivalence class [x] is a neighbourhood of it.

• Referencias bibliográficas
  • L. S. Block and W. A. Coppel, Dynamics in One Dimension, Volume 1513 of Lecture Notes in Mathematics, Springer-Verlag, Berline, 1992. https://doi.org/10.1007/BFb0084762
  • L. Block and E. Coven, Topological conjugacy and transitivity for a class of piecewise monotone maps of the interval, Trans. Amer. Math. Soc....
  • M. Brin and G. Stuck, Introduction to Dynamical Systems, Cambridge University Press, 2002. https://doi.org/10.1017/CBO9780511755316
  • R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley Publishing Company Advanced Book Program, Redwood City, CA, second...
  • R. A. Holmgren, A First Course in Discrete Dynamical Systems, Springer-Verlag, New York, 1996. https://doi.org/10.1007/978-1-4419-8732-7
  • S. Sai, Symbolic dynamics for complete classification, Ph.D Thesis, University of Hyderabad, 2000.
  • B. Sankara Rao, I. Subramania Pillai and V. Kannan, The set of dynamically special points, Aequationes Mathematicae 82, no. 1-2 (2011), 81-90....
  • A. N. Sharkovskii, Coexistence of cycles of a continuous map of a line into itself, Ukr. Math. Z. 16 (1964), 61-71.