Topological characterization of the hyperbolic maps in the Sine family

TL;DR

This paper provides a topological classification of hyperbolic sine family maps with super-attracting cycles, enhancing understanding of their dynamical structures in complex analysis.

Contribution

It offers a novel topological characterization of hyperbolic sine maps with super-attracting cycles, a previously unclassified aspect in complex dynamics.

Findings

Topological classification of hyperbolic sine maps established

Characterization of super-attracting cycles in these maps

Enhanced understanding of sine family dynamics

Abstract

The purpose of this paper is to establish a topological characterization of all the hyperbolic maps in the Sine family $\{\lambda \sin(z) \:\big{|}\:\lambda \ne 0\}$ which have super-attracting cycles.