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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/713| Chaos and Period Forcing For a Family of Piecewise Monotonic Real-Valued Functions | |
| SOPHEA SIN | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Chaotic behavior | |
| In this work we consider a family of one-real parameter of piecewise monotone real-valued functions given by〖 f〗_b (x)=℘(x)+b, where b is a real parameter and ℘denotes the Weierstrass ℘ function defined over a real square lattice and restricted over the real line. Each element in the familyf_bdefines a periodic function over the real line with singularities at the integer multiples of its real period. When restricted to a fundamental interval, the family f_b exhibits some dynamical similarities to the quadratic family x^2+c. One of the main problems addressed in this thesis is to show that under certain conditions on the parameter where b and the lattice, f_bacts over the real line as a chaotic dynamical system. The second problem considered in this work is related to Sharkovskii’s Theorem, one of the most celebrated theorems in real dynamics. This theorem states a period forcing result: if f is a continuous function over the real line that has a periodic point of period n, then it must also have a periodic point of period k, with smaller k than n in the Sharkovskii ordering. Taking into account that each f_bis no longer continuous in the whole real line, we provide a partial period forcing result for the family f_b following Sharkovskii’s ordering. | |
| 06-10-2017 | |
| Tesis de maestría | |
| Inglés | |
| OTRAS | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
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| Fichero | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| TE 642.pdf | 1.16 MB | Adobe PDF | Visualizar/Abrir |