Browsing by Author "Bray, Kasey"
Now showing 1 - 2 of 2
- Results Per Page
- Sort Options
Item Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions(2020) Bray, Kasey; Dwyer, Jerry (TTU); Barnard, Roger W. (TTU); Williams, G. Brock (TTU)The dynamical systems of trigonometric functions are explored, with a focus on tz=tanz and the fractal image created by iterating the Newton map, Ftz, of tz. The basins of attraction created from iterating Ftz are analyzed, and some bounds are determined for the primary basins of attraction. We further prove x- A nd y-axis symmetry of the Newton map and explore the nature of the fractal images.Item Iterations of the newton map of tan(z)(2013-05) Bray, Kasey; Dwyer, Jerry F.; Barnard, Roger W.; Williams, G. BrockThe 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.