The 9th Workshop on Hamiltonian Systems and Related Topics

Scope and Aim:

Hamiltonian systems have attarcted central attention in dynamical systems since the time of Poincaré. They are of special characteristics in dynamical systems but exhibit interesting, complicated phenomena such as chaos and Arnold diffusion. In addition, their solutions are not generally given in closed forms, and many of them are believed to be nonintegrable. Differential Galois theory provides a basis for the Morales-Ramis theory, which is a powerful tool in proving their nonintegrability, and has also made great success in many other applications, e.g., integrable PDEs such as the KdV equation, quantum mechanics, and bifurcations of solitary waves in PDEs. This workshop aims to discuss recent progress and future directions in Hamiltonian systems and related topics, especially in theoretical results on complicated phenomena and applications of differential Galois theory.

Program:

March 4 (Tuesday)

• 9:30-9:40
  Opening

• 9:40-10:40
  Andrzej Maciejewski (University of Zielona Gola, Poland)
  Non-integrability of the n body problem

• 11:00-12:00
  Shoya Motonaga (Ritsumeikan University, Japan)
  Perturbation approaches to non-existence of first integrals and commutative vector fields in continuous dynamical systems

• 12:00-13:40
  Lunch

• 13:40-14:40
  Thierry Combot (University of Burgundy)
  Restricted integrability and Liouville Arnold integrability

• 15:00-16:00
  Teresa Crespo (University of Barcelona, Spain)
  Algebraic aspects of real differential Galois theory

• 16:20-17:20
  Zbigniew Hajto (Jagiellonian University, Poland)
  Tame topology and non-integrability of real dynamical systems

• 18:00-20:00
  Welcome Party
  Cafe Restaurant Camphora (inside the Main Campus of Kyoto University)

March 5 (Wednesday)

• 10:00-11:00
  Juan J. Morales-Ruiz (Universidad Politecnica de Madrid, Spain)
  Semiclassical constant elasticity variance option pricing model: An analytical approach

• 11:20-12:20
  Kazuyuki Yagasaki (Kyoto University, Japan)
  Heteroclinic transition motions and nonintegrability for periodic perturbations of conservative systems

• 12:20-14:20
  Lunch

• 14:20-15:20
  Amadeu Delshams (Universidad Politecnica de Catalunya, Spain)
  Semi-analytic construction of global transfers between quasi-periodic orbits in the spatial R3BP

• 15:40-16:40
  Marian Gidea (Yeshiva University, USA)
  Hamiltonian instability in the elliptic Hill four-body problem: geometric method and numerical verification

• 17:00-18:00
  Pau Martin (Universidad Politecnica de Catalunya, Spain)
  Chaotic phenomena around L4 in the RPC3BP beyond the Routh mass ratio

March 6 (Thursday)

• 10:00-11:00
  Inma Baldoma (Universidad Politecnica de Catalunya, Spain)
  Chaoticity of generic analytic convex billiards

• 11:20-12:20
  Rafael Ramirez-Ros (Universidad Politecnica de Catalunya, Spain)
  High-order persistence of resonant caustics in perturbed circular billiards

• 12:20-14:20
  Lunch

• 14:20-15:20
  Kuo-Chang Chen (National Tsing Hua University, Taiwan)
  Some quantitative aspects of action minimizing solutions

• 15:40-16:40
  Mitsuru Shibayama (Kyoto University, Japan)
  Variational construction of orbits realizing symbolic sequences in the planar Sitnikov problem

• 16:40
  Closing