Abstract
In the paper all three and five periodic orbits of certain (known and a bit less known) quadratic and cubic polynomials as well as polynomials of order greater than 4 are generated. Other periodic orbits are also discussed here. The basic polynomials considered in this paper are the minimal polynomials of \(2\mathop {\cos } \frac{2\pi }{2n - 1}\) or \(2\mathop {\sin } \frac{2\pi }{2n - 1}\) for every \(n = 4,5,6,7,8\). The concept of n-periodic trigonometric orbits is introduced. Also generalizations of Benedetto identities are presented.
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Wituła, R., Hetmaniok, E., Słota, D., Trawiński, T., Kołton, W. (2015). On the Three, Five and Other Periodic Orbits of Some Polynomials. In: Gołębiowski, L., Mazur, D. (eds) Analysis and Simulation of Electrical and Computer Systems. Lecture Notes in Electrical Engineering, vol 324. Springer, Cham. https://doi.org/10.1007/978-3-319-11248-0_8
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