Fixed points, symmetries, and bounds for basins of attraction of complex trigonometric functions (Q779954)

Summary: 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 \(t (z)\). The basins of attraction created from iterating \(F_t(z)\) 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.