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On the existence of doubly symmetric "Schubart-like" periodic orbits
A constructive proof of the existence of a semi-conjugacy for a one dimensional map
1. | School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287-1804, United States |
2. | Department of Financial and Computational Mathematics, Providence University, Taichung 43301, Taiwan |
References:
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, IEEE standard for floating-point arithmetic,, The Institute of Electrical and Electronics Engineers, (2008).
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Ll. Alsedà, J. Llibre and M. Misurewicz, "Combinatorial Dynamics and Entropy in Dimension One," 2nd edition, Advanced Series in Nonlinear Dynamics, 5, World Scientific Publishing Co., Inc., River Edge, NJ, 2000. |
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J. Banks, V. Dragan and A. Jones, "Chaos: A Mathematical Introduction," Australian Mathematical Society Lecture Series, 18, Cambridge University Press, Cambridge, 2003. |
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K. M. Brucks and H. Bruin, "Topics from One-Dimensional Dynamics," London Mathematical Society Student Texts, 62, Cambridge University Press, Cambridge, 2004. |
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R. L. Devaney, "An Introduction to Chaotic Dynamical Systems," 2nd edition, Addison-Wesley Studies in Nonlinearity, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989. |
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N. A. Fotiades and M. A. Boudourides, Topological conjugacies of piecewise monotone interval maps, International Journal of Mathematics and Mathematical Sciences, 25 (2001), 119-127.
doi: 10.1155/S0161171201004343. |
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P. Henrici, "Essentials of Numerical Analysis with Pocket Calculator Demonstrations," John Wiley & Sons, Inc., New York, 1982. |
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J. Milnor and W. Thurston, On iterated maps of the interval, in "Dynamical Systems" (ed. J. C. Alexander) (College Park, MD, 1986-87), Lecture Notes in Mathematics, 1342, Springer, Berlin, (1988), 465-563. |
[9] |
W. Parry, Symbolic dynamics and transformations of the unit interval, Transactions of the American Mathematical Society, 122 (1966), 368-378.
doi: 10.1090/S0002-9947-1966-0197683-5. |
show all references
References:
[1] |
, IEEE standard for floating-point arithmetic,, The Institute of Electrical and Electronics Engineers, (2008).
|
[2] |
Ll. Alsedà, J. Llibre and M. Misurewicz, "Combinatorial Dynamics and Entropy in Dimension One," 2nd edition, Advanced Series in Nonlinear Dynamics, 5, World Scientific Publishing Co., Inc., River Edge, NJ, 2000. |
[3] |
J. Banks, V. Dragan and A. Jones, "Chaos: A Mathematical Introduction," Australian Mathematical Society Lecture Series, 18, Cambridge University Press, Cambridge, 2003. |
[4] |
K. M. Brucks and H. Bruin, "Topics from One-Dimensional Dynamics," London Mathematical Society Student Texts, 62, Cambridge University Press, Cambridge, 2004. |
[5] |
R. L. Devaney, "An Introduction to Chaotic Dynamical Systems," 2nd edition, Addison-Wesley Studies in Nonlinearity, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989. |
[6] |
N. A. Fotiades and M. A. Boudourides, Topological conjugacies of piecewise monotone interval maps, International Journal of Mathematics and Mathematical Sciences, 25 (2001), 119-127.
doi: 10.1155/S0161171201004343. |
[7] |
P. Henrici, "Essentials of Numerical Analysis with Pocket Calculator Demonstrations," John Wiley & Sons, Inc., New York, 1982. |
[8] |
J. Milnor and W. Thurston, On iterated maps of the interval, in "Dynamical Systems" (ed. J. C. Alexander) (College Park, MD, 1986-87), Lecture Notes in Mathematics, 1342, Springer, Berlin, (1988), 465-563. |
[9] |
W. Parry, Symbolic dynamics and transformations of the unit interval, Transactions of the American Mathematical Society, 122 (1966), 368-378.
doi: 10.1090/S0002-9947-1966-0197683-5. |
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