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Period 3 and chaos for unimodal maps
1. | Department of Applied Mathematics, Chung Yuan Christian University, Chungli, Taiwan, Taiwan |
2. | Department of Financial and Computational Mathematics, Providence University, Taichung, Taiwan |
References:
[1] |
B. Aulbach and B. Kieninger, An elementary proof for hyperbolicity and chaos of the logistic maps, J. Difference Eqns. Appl., 10 (2004), 1243-1250. |
[2] |
L. Block and W. A. Coppel, Dynamics in One Dimension, Lecture Notes in Mathematics 1513, Springer-Verlag, New York, 1992. |
[3] |
R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Second edition. Addison-Wesley Studies in Nonlinearity. Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989. |
[4] |
B. Hasselblatt and A. Katok, A First Course in Dynamics: With a Panorama of Recent Developments, Cambridge University Press, New York, 2003. |
[5] |
R. L. Kraft, Chaos, Cantor sets, and hyperbolicity for the logistic maps, Amer. Math. Monthly, 106 (1999), 400-408.
doi: 10.2307/2589144. |
[6] |
T.-Y. Li and J. Yorke, Period three implies chaos, Amer. Math. Monthly, 82 (1975), 985-992.
doi: 10.2307/2318254. |
[7] |
A. N. Sharkovsky, Co-existence of cycles of a continuous mapping of the line into itself, Ukrain. Math. J., 16 (1964), 61-71. |
[8] |
D. Singer, Stable orbits and bifurcation of maps of the interval, SIAM J. Appl. Math., 35 (1978), 260-267.
doi: 10.1137/0135020. |
[9] |
X. Zhang, Y. Shi and G. Chen, Some properties of coupled-expanding maps in compact sets, Proc. Amer. Math. Soc., 141 (2013), 585-595.
doi: 10.1090/S0002-9939-2012-11339-5. |
show all references
References:
[1] |
B. Aulbach and B. Kieninger, An elementary proof for hyperbolicity and chaos of the logistic maps, J. Difference Eqns. Appl., 10 (2004), 1243-1250. |
[2] |
L. Block and W. A. Coppel, Dynamics in One Dimension, Lecture Notes in Mathematics 1513, Springer-Verlag, New York, 1992. |
[3] |
R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Second edition. Addison-Wesley Studies in Nonlinearity. Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989. |
[4] |
B. Hasselblatt and A. Katok, A First Course in Dynamics: With a Panorama of Recent Developments, Cambridge University Press, New York, 2003. |
[5] |
R. L. Kraft, Chaos, Cantor sets, and hyperbolicity for the logistic maps, Amer. Math. Monthly, 106 (1999), 400-408.
doi: 10.2307/2589144. |
[6] |
T.-Y. Li and J. Yorke, Period three implies chaos, Amer. Math. Monthly, 82 (1975), 985-992.
doi: 10.2307/2318254. |
[7] |
A. N. Sharkovsky, Co-existence of cycles of a continuous mapping of the line into itself, Ukrain. Math. J., 16 (1964), 61-71. |
[8] |
D. Singer, Stable orbits and bifurcation of maps of the interval, SIAM J. Appl. Math., 35 (1978), 260-267.
doi: 10.1137/0135020. |
[9] |
X. Zhang, Y. Shi and G. Chen, Some properties of coupled-expanding maps in compact sets, Proc. Amer. Math. Soc., 141 (2013), 585-595.
doi: 10.1090/S0002-9939-2012-11339-5. |
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