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  Far East Journal of Dynamical Systems  
 ISSN: 0972-1118
 
 
 

     Far East Journal of Dynamical Systems
    Volume 10, Issue 2, Pages 185 - 201 (June 2008)


ON DYNAMICS OF CIRCLE MAPS

Puneet Sharma (India) and Anima Nagar (India)

Received August 22, 2007; Revised October 23, 2007

References:



[1] Lluís Alsedà, Jaume Llibre and M. Misiurewicz, Combinatorial dynamics and entropy in dimension one, 2nd ed., Advanced Series in Nonlinear Dynamics, 5, World Scientific Publishing Co., Inc., River Edge, NJ, 2000.

[2] John Banks, Chaos for induced hyperspace maps, Chaos Solitons Fractals 25 (2005), 681-685.

[3] L. S. Block and W. A. Coppel, Dynamics in one dimension, Lecture Notes in Mathematics, 1513, Springer-Verlag, Berlin, 1992.

[4] L. Block, Ethan Coven, Irene Mulvey and Z. Nitecki, Homoclinic and nonwandering points for maps of the circle, Ergodic Theory Dynam. Systems 3 (1983), 521-532.

[5] L. Block, E. M. Coven and Z. Nitecki, Minimizing topological entropy for maps of the circle, Ergodic Theory Dynam. Systems 1 (1981), 145-149.

[6] L. Block, J. Guckenheimer, M. Misiurwicz and L. S. Young, Periodic points and topological entropy of one-dimensional maps, Global Theory of Dynamical Systems, pp. 18-34, Lecture Notes in Math., 819, Springer, Berlin, 1980.

[7] J. S. Cánovas and A. Linero, On the dynamics of composition of commuting interval maps, J. Math. Anal. Appl. 305 (2005), 296-303.

[8] Naotsugu Chinen, Circle maps having an infinite omega-limit set which contains a periodic orbit have positive topological entropy, Proc. Amer. Math. Soc. 131 (2003), 3547-3551.

[9] Ethan M. Coven and Irene Mulvey, Transitivity and the centre for maps of the circle, Ergodic Theory Dynam. Systems 6 (1986), 1-8.

[10] L. S. Efremova, Periodic orbits and a degree of a continuous map of a circle, Diff. and Integr. Equations (Gor’kii) 2 (1978), 109-115 (in Russian).

[11] Anima Nagar, V. Kannan and Karnam Srinivas, Some simple conditions implying topological transitivity on interval maps, Aequationes Math. 67 (2004), 201-204.

[12] Heriberto Román-Flores, A note on transitivity in set-valued discrete systems, Chaos Solitons Fractals 17 (2003), 99-104.

[13] Stephen Silverman, On maps with dense orbits and the definition of chaos, Rocky Mountain J. Math. 22 (1992), 353-375.

Keywords and phrases: circle maps, lift, periodic point, transitivity, sensitive, topological entropy, commuting maps.

 


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