Iterations of the newton map of tan(z)
| dc.contributor.committeeChair | Dwyer, Jerry F. | |
| dc.contributor.committeeMember | Barnard, Roger W. | |
| dc.contributor.committeeMember | Williams, G. Brock | |
| dc.creator | Bray, Kasey | |
| dc.date.available | 2013-05-24T18:41:42Z | |
| dc.date.issued | 2013-05 | |
| dc.description.abstract | The dynamical systems of trigonometric functions are explored, with a focus on t(z)=tan(z) and the fractal image created by iterating the Newton map, F_t (z), of t(z). As a point of reference we present Newton’s method applied to polynomials and the iterations of families of trigonometric functions. The basins of attraction created from iterating F_t (z) are analyzed and, in an effort to determine the fate of each seed value, bounds are placed within the primary basins of attraction. We further prove x and y-axis symmetry of the function, and explore the infinite nature of the fractal images. Lastly, Newton iterations of the family〖 z〗^k tan(z) are explored in comparison with F_t (z) and Householder’s methods are discussed. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.slug | 2346/ETD-TTU-2013-05-1195 | |
| dc.identifier.uri | http://hdl.handle.net/2346/48913 | |
| dc.language.iso | eng | |
| dc.subject | Newton's method | |
| dc.subject | Dynamics of trigonometric functions | |
| dc.subject | Tan(z) | |
| dc.title | Iterations of the newton map of tan(z) | |
| dc.type | Thesis | |
| thesis.degree.department | Mathematics and Statistics | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Texas Tech University | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science |