Exploring Topological Transitivity in Families of Functions

TL;DR

This paper investigates conditions for topological transitivity in families of continuous and holomorphic functions, providing new criteria and an alternative proof of Montel's three point theorem using properties of expanding meromorphic functions.

Contribution

It introduces new criteria for topological transitivity and offers an alternative proof of Montel's three point theorem based on expanding meromorphic functions.

Findings

Established criteria for topological transitivity in function families

Provided an alternative proof of Montel's three point theorem

Linked properties of expanding meromorphic functions to topological dynamics

Abstract

We have established various criteria for the topological transitivity of families of continuous (holomorphic) functions. Furthermore, by leveraging the properties of expanding families of meromorphic functions, we offer an alternative proof of Montel's three point theorem.