Dynamics of Iterations of the Newton Map of sin(z)

Abstract

The dynamical systems of trigonometric functions are explored, with a focus on (Formula presented.) and the fractal image created by iterating the Newton map, (Formula presented.), of (Formula presented.). The basins of attraction created from iterating (Formula presented.) are analyzed, and some bounds are determined for the primary basins of attraction. We further prove (Formula presented.) and (Formula presented.) -axis symmetry of the Newton map as well as some interesting results on periodic points on the real axis.

Description

© 2024 by the authors. cc-by

Keywords

complex dynamics, Newton map, trigonometric functions

Citation

Cloutier, A., Dwyer, J., Barnard, R.W., Stone, W.D., & Williams, G.B.. 2024. Dynamics of Iterations of the Newton Map of sin(z). Symmetry, 16(2). https://doi.org/10.3390/sym16020162

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