Complex Dynamics 

Speaker: Sukanta Das (Ph.D. Student, IIT Bhubaneswar)

Lecture - 3

Title: Some Properties of the Julia Set and Structure of the Fatou Components

Date: 19th April, 2025 (Saturday)

Time: 11:00 AM - 12:00 PM (IST)

Abstract: In this talk, we will explore the relationship between periodic points and the Julia set of a rational map of degree at least two. We will also discuss the expansivity property of the Julia set. Following that, we will discuss various types of Fatou components and introduce two new components arising in the context of transcendental entire functions. Additionally, we will present some results concerning the structure of the Fatou set.

Lecture - 2

Title: Iteration of Rational Functions

Date: 12th April, 2025 (Saturday)

Time: 11:00 AM - 12:00 PM (IST)

Abstract: In this talk, we will explore the iteration of rational functions, with a particular focus on how the dynamics of a polynomial are influenced by the forward orbit of a critical point. We will then examine key properties of the Julia set associated with rational maps of degree at least two. Following that, we will discuss the classification of periodic points and the various types of Fatou components. Throughout the talk, we will also highlight how these results and ideas extend to the setting of transcendental entire functions.

Lecture - 1

Title: An Invitation to Complex Dynamics: Iterating Functions in the Complex Plane

Date: 5th April, 2025 (Saturday) 

Time: 11:00 AM - 12:00 PM (IST) 

Abstract: In this talk, we will explore the fundamentals of iterated complex functions, focusing on the dynamics that arise from repeated application. We will delve into the properties of Fatou sets (regions of stability), and Julia sets (regions of chaos), highlighting their significance in understanding complex behavior. Additionally, we will analyze some functions to visualize and interpret their iterative behavior in the complex plane.