Numbering Code	G-INF04 53425 LJ10 G-INF04 53425 LJ55 G-INF04 53425 LJ57	Year/Term	2022 ・ Second semester
Number of Credits	2	Course Type	Lecture
Target Year		Target Student
Language	Japanese	Day/Period	Tue.2
Instructor name	SHIBAYAMA MITSURU (Graduate School of Informatics Associate Professor)
Outline and Purpose of the Course	Hamiltonian dynamical systems are dynamical systems including classical mechanics, and important field as mathematical theory and application. In the lecture, we first explain the definition of integrability in the sense of Liouville, and its property. Next, we introduce Poincare's theorem stating the nonintegrability and the existence of invariant tori for near-integrable systems. Finally, we survey some related topics.
Course Goals	Students will understand the theory of integrable Hamiltonian systems and perturbation theory, and will be able to apply the perturbation theory to models which can be represented as near-integrable systems.
Schedule and Contents	1. Differential forms 2. Examples of Hamiltonian systems 3. Canonical transforms 4. Definition and examples of integrable systems 5. Liouville-Arnold theorem and action-angle coordinates 6. Proof of Liouville-Arnold theorem 7. Non-integrability of near-integrable systems 8. Diophantine condition 9. KAM theorem 10. Proof of KAM theorem 11. Application of KAM theorem to forced pendulum 12. Birkhoff normal form 13. Stability of Lagrange points of the restricted 3-body problem 14. Arnold diffusion 15. Aubry-Mather theory
Evaluation Methods and Policy	The final grade will be determined by several written reports.
Course Requirements	None
Study outside of Class (preparation and review)	Students are required to review each lecture.
References, etc.	Stable and Random Motions in Dynamical Systems, J. Moser, (Princeton University Press), ISBN:9780691089102