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International Journal of Latest Research in Science and Technology

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Properties on Bifurcation and Topological Entropy in Symbolic dynamics

Research Paper Open Access

International Journal of Latest Research in Science and Technology Vol.8 Issue 2, pp 1-7,Year 2019

PROPERTIES ON BIFURCATION AND TOPOLOGICAL ENTROPY IN SYMBOLIC DYNAMICS

Sankar Haloi , Prem Chand Sharma

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Received : 06 March 2019; Accepted : 26 March 2019 ; Published : 30 April 2019

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Abstract

The prime objectives of this paper are to establish Feigenbaum bifurcation universality on the population model : where and is a positive parameter; and to obtain topological entropy on unimodal map: f(x) = λx(1-x), x ∈[0,1] , λ∈ (1,4]

Key Words   
Shift map, Topological entropy, Feigenbaum universality
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References
  1. Aoki.N and K.Hiraide, Topological Theory of Dynamical Systems, Recent Advances.North-Holland Mathematical Library,1994.
  2. Balibrea F., Snoha L., Topological Entropy of Devaney Chaotic Maps, Topology Appl, 133, pp 225-239,2003.
  3. Bhaumik I. and Choudhury B.S.,The Shift Map and the Symbolic Dynamics and Application of Topological Conjugacy, Journal of Physical Sciences, vol.13, 149-160, 2009.
  4. Bowen R.,  Topological Entropy and Axiom A, Global Analysis, ProcSympos, Pure Math ,Amer. Math. Soc, 14: pp23-42, 1970.
  5. Bowen R., Topological entropy for  non  compact  sets,  Trans. Amer. Math. Soc.184; 125-136, 1973.
  6. Chow, S. N. and Hale, J. K., Methods of Bifurcation Theory, Spinger- Verlag,  1982.
  7. Clark R., Dynamical Systems: Stability, Symbolic Dynamics, and Chaos, CRC Press,  Inc 1995
  8. Ca´novas J.S  and  Rodr´ıguez J.M, “ Topological entropy of maps on the real line”. Topology Appl., 153(5-6):735–746. ISSN 0166-8641, 2005
  9. Douglass Lind and Brian Marcas,   An Introduction to Symbolic Dynamics and         Coding,Cambridge University Press,1999.
  10. Kurka P,  Topological and Symbolic Dynamics, SocieteMathematique de France, 2003.
  11. Kitchens B. P,.Symbolic Dynamics-One Sided, Two Sided and Countable State Markov Shifts, Universitext, Springer Verlag, Berlin.1998
  12. SmitalJ ., Chaotic Functions with Zero Topological Entropy, Trans. Amer. Math.Soc, 297 : pp269-282,1986.
  13. Vul, E. B., Ya. G. S. and Khanin, K. M., Feigenbaum Universality and the   thermodynamic Form,alism, and UsphekiMat.Nauk 39:3(1984)3-37, Russian Math  Surveys 39:3(1984),1-40
To cite this article

Sankar Haloi , Prem Chand Sharma , " Properties On Bifurcation And Topological Entropy In Symbolic Dynamics ", International Journal of Latest Research in Science and Technology . Vol. 8, Issue 2, pp 1-7 , 2019


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