Boundedness of Fatou components of the family f(z)=\lambda sin(z)+a

TL;DR

This paper investigates the conditions under which Fatou components of the sine family of functions remain bounded, focusing on cases where the parameter has modulus greater than one and the map is post-critically bounded.

Contribution

It provides new insights into the boundedness of Fatou components for sine functions with specific parameter constraints, extending previous understanding.

Findings

Fatou components are bounded when |λ| > 1 and the map is post-critically bounded

The paper characterizes the relationship between parameter values and Fatou component boundedness

Results contribute to the classification of dynamical behaviors in sine family functions

Abstract

In this paper we discuss the boundedness of the Fatou components for the sine family and the extended sine family, mainly when the parameter \lambda has modulus greater than 1 and the map is post-critically bounded.