Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions
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 fu...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2020/1853467 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832553981249847296 |
|---|---|
| author | Kasey Bray Jerry Dwyer Roger W. Barnard G. Brock Williams |
| author_facet | Kasey Bray Jerry Dwyer Roger W. Barnard G. Brock Williams |
| author_sort | Kasey Bray |
| collection | DOAJ |
| description | 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- and y-axis symmetry of the Newton map and explore the nature of the fractal images. |
| format | Article |
| id | doaj-art-ea08fd18aa884ab3b6fd8bc5a089ea48 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ea08fd18aa884ab3b6fd8bc5a089ea482025-02-03T05:52:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/18534671853467Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric FunctionsKasey Bray0Jerry Dwyer1Roger W. Barnard2G. Brock Williams3Montgomery Bell Academy, Nashville, TN 37205, USATexas Tech University, Lubbock, TX 79409, USATexas Tech University, Lubbock, TX 79409, USATexas Tech University, Lubbock, TX 79409, USAThe 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- and y-axis symmetry of the Newton map and explore the nature of the fractal images.http://dx.doi.org/10.1155/2020/1853467 |
| spellingShingle | Kasey Bray Jerry Dwyer Roger W. Barnard G. Brock Williams Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions International Journal of Mathematics and Mathematical Sciences |
| title | Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions |
| title_full | Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions |
| title_fullStr | Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions |
| title_full_unstemmed | Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions |
| title_short | Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions |
| title_sort | fixed points symmetries and bounds for basins of attraction of complex trigonometric functions |
| url | http://dx.doi.org/10.1155/2020/1853467 |
| work_keys_str_mv | AT kaseybray fixedpointssymmetriesandboundsforbasinsofattractionofcomplextrigonometricfunctions AT jerrydwyer fixedpointssymmetriesandboundsforbasinsofattractionofcomplextrigonometricfunctions AT rogerwbarnard fixedpointssymmetriesandboundsforbasinsofattractionofcomplextrigonometricfunctions AT gbrockwilliams fixedpointssymmetriesandboundsforbasinsofattractionofcomplextrigonometricfunctions |