The 8th Workshop on Hamiltonian Systems and Related Topics

August 28-29, 2023

Graduate School of Informatics, Kyoto University

(Lecture Room 4 (3F), Research Building No. 8, Main Campus)

Organizers:
Mitsuru Shibayama (Kyoto Univeristy)
Kazuyuki Yagasaki (Kyoto University)




---




Scope and Aim:

Differential Galois Theory has made great success in many applications, e.g., the nonintegrability of dynamical systems including the N-body problems, integrable PDEs such as the KdV equation, quantum mechanics, and bifurcations of solitary waves in PDEs. Celstial Mechanics is one of central topics in dynamical systems since Poincare's time. This workshop aims to discuss recent progress and future directions in Hamiltonian systems and related topics, especially in applications of Differential Galois Theory and Celestial Mechanics.




Program:

(The talks of the speakers with asterisk will be given online.)

August 28

• 9:55

  Opening



• 10:00-11:00

  Holger Dullin (University of Sydney)

  On the stability of the 3-body problem



• 11:20-12:20

  Xiang Zhang (Shanghai Jiaotong University)

  Varieties and analytic normalizations of partly integrable systems near a periodic orbit



• 12:20-14:20

  Lunch



• 14:20-15:20

  Thierry Combot (University of Burgundy)

  Integrability and meromorphic solutions



• 15:40-16:40

  Zbigniew Hajto* (Jagiellonian University)

  Real Liouvillian extensions of partial differential fields



• 17:00-18:00

  Maria-Angeles Zurro* (Universidad Autonóma de Madrid)

  Burchnall-Chaundy polynomials for matrix ODOs and Picard-Vessiot Theory




August 29

• 10:00-11:00

  Shoya Motonaga (Ritsumeikan University)

  Nonintegrability of nearly integrable dynamical systems near regular level sets



• 11:20-12:20

  Mitsuru Shibayama (Kyoto University)

  Non-integrability criterion for homogeneous Hamiltonian systems via blowing-up theory



• 12:20-14:20

  Lunch



• 14:20-15:20

  Juan José Morales-Ruiz (Universidad Politecnica de Madrid)

  Semiclassical quantification of some two degree of freedom potentials: a differential Galois approach



• 15:40-16:40

  Kazuyuki Yagasaki (Kyoto University)

  Nonintegrability of the restricted three-body problem



• 17:00-18:00

  Alexei Tsygvintsev* (École Normale Supérieure de Lyon)

  On some collinear configurations in the planar three-body problem



• 18:00

  Closing





---




Abstracts




---



This workshop is supported by

• JSPS KAKENHI for Scientific Research (B) Grant Number JP22H01138
  (PI: Kazuyuki Yagasaki)




---



Hamiltonian Dynamical Systems Seminar (in Japanese)

Latest Updating is on August 27, 2023.