Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions

Abstract

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.