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On the existence of doubly symmetric "Schubartlike" periodic orbits
A constructive proof of the existence of a semiconjugacy for a one dimensional map
1.  School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 852871804, United States 
2.  Department of Financial and Computational Mathematics, Providence University, Taichung 43301, Taiwan 
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, IEEE standard for floatingpoint 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," 2^{nd} 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. 
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K. M. Brucks and H. Bruin, "Topics from OneDimensional 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," 2^{nd} edition, AddisonWesley Studies in Nonlinearity, AddisonWesley 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), 119127. 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, 198687), Lecture Notes in Mathematics, 1342, Springer, Berlin, (1988), 465563. 
[9] 
W. Parry, Symbolic dynamics and transformations of the unit interval, Transactions of the American Mathematical Society, 122 (1966), 368378. doi: 10.1090/S00029947196601976835. 
show all references
References:
[1] 
, IEEE standard for floatingpoint arithmetic,, The Institute of Electrical and Electronics Engineers, (2008). 
[2] 
Ll. Alsedà, J. Llibre and M. Misurewicz, "Combinatorial Dynamics and Entropy in Dimension One," 2^{nd} 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 OneDimensional Dynamics," London Mathematical Society Student Texts, 62, Cambridge University Press, Cambridge, 2004. 
[5] 
R. L. Devaney, "An Introduction to Chaotic Dynamical Systems," 2^{nd} edition, AddisonWesley Studies in Nonlinearity, AddisonWesley 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), 119127. 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, 198687), Lecture Notes in Mathematics, 1342, Springer, Berlin, (1988), 465563. 
[9] 
W. Parry, Symbolic dynamics and transformations of the unit interval, Transactions of the American Mathematical Society, 122 (1966), 368378. doi: 10.1090/S00029947196601976835. 
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