The 2023 VIASM Workshop on Dynamical Systems and Related Topics will be held at the Vietnam Institute for Advanced Study in Mathematics (VIASM) from Jan 3 (Tue) - 6 (Fri), 2023.

The purpose of this workshop is to introduce what our research group is currently working on dynamical systems (induced by various equations) and related topics, share the ideas with each other based on the presentations, and finally lay the foundation for our joint research among the participants.

We hope this workshop will provide an environment where we can find interesting problems in the theory of dynamical systems and related topics. We think this kind of event is important for young researchers and graduate students.

Invited Speakers

- Cung The Anh (Hanoi Nat Uni of Edu)

- Lee Keonhee (Chungnam Nat Uni)

- Lee Manseob (Mokwon Uni)

- Morales Carlos (Federal Uni of Rio de Janeiro)

- Nguyen Thieu Huy (Hanoi Uni of Sci and Tech)

- Tran Dinh Ke (Hanoi Nat Uni of Edu)

- Vu Hoang Linh (VNU-Hanoi Uni of Sci)

Organizing Committee

- Nguyen Huu Du: (Chair) VNU-Hanoi University of Science

- Cung The Anh: Hanoi National University of Education

- Le Minh Ha: Vietnam Institute for Advanced Study in Mathematics

- Lee Keonhee: Chungnam National University

- Nguyen Thieu Huy: Hanoi University of Science and Technology

Contact

If you have any questions, please feel free to contact

• Nguyen Ngocthach, email: ngngocthach91@gmail.com

Venue/Location: VIASM

Lecturer: Prof. Lee Keonhee (Chungnam National University)

Tentative Schedule

The lecture will be held every Monday, Wednesday, and Friday from 9:30 a.m to 11:30 a.m from November 21 to December 2, 2022.

Registration here:

https://docs.google.com/forms/d/e/1FAIpQLSddmTsAd-RctllOK4WvvCFGuSAEW--TdCerfE0jRkLTvrq5ww/viewform?usp=pp_url

Deadline for registration: November 14, 2022.

Who can attend the mini-course?

We welcome graduate students and scholars who are interested in the theory of dynamical systems. We are going to give lectures from the basic knowledge in topology and measure theory so that the participants can fully understand the lectures.

How do we prepare the references?

We will provide you a copy of the book entitled in Topological Dynamics from Measurable Viewpoint which I have been composing with my colleagues, Dr. Ngocthach Nguyen and Prof C.A. Morales, in the first hour of the lecture.

Introduction to the mini-course

It is not easy to find an exact solution of a system of differential equations (ODEs or PDEs). Even though such an analytic solution of the system can be found, it is more difficult to understand the “qualitative information” of the solution curves. Finally, Poincaré introduced a notion of dynamical system to study the qualitative information of all the solution curves of the system. The main goal of the theory of dynamical systems is to understand the long time behavior of solution curves of the systems in topological, differentiable, and measurable viewpoints. In this mini-course, we are going to study some basic knowledge in the theory of topological dynamics, and extend them from measurable viewpoint.

Lecture 1: Why dynamical systems? (Nov 21, Mon)

In this lecture, we present motivation, classification and basic knowledge of dynamical systems.

Lecture 2: Fundamental concepts in topological dynamics (Nov 23, Wed)

We recall some basic notions and fundamental results in topological dynamics.

Lecture 3: Expansive measures (Nov 25, Fri)

We introduce a notion of expansive measures for dynamical systems, and discuss fundamental properties of expansive measures.

Lecture 4: Shadowable measures (Nov 28, Mon)

We introduce a notion of shadowable measures for dynamical systems, and show that a dynamical system has the shadowing property if and only if every invariant measure is shadowable.

Lecture 5: Topological stability (Nov 30, Wed)

We introduce a notion of topologically stable measures for dynamical systems, and present a measurable version of Walters’ stability theorem.

Lecture 6: Spectral decomposition (Dec 2, Fri)

We present a measurable version of Smale’s spectral decomposition theorem which is most important in the theory of topological dynamics.

Contact

If you have any questions, please feel free to contact

• Nguyen Ngocthach, email: ngngocthach91@gmail.com