Researcher Database

（Last updated : 2024-04-05 09:52:06）

MOTONAGA SHOYA

Department / Course College of Science and Engineering Department of Mathematical Sciences

Title / Position Assistant Professor

Academic background
1.	2018/10～2021/11	Doctoral Program (2nd Semester) │ Department of Applied Mathematics and Physis │ Graduate School, Division of Information and Communication │ Kyoto University
2.	2017/04～2018/09	Master Course │ Department of Applied Mathematics and Physis │ Graduate School, Division of Information and Communication │ Kyoto University
3.	2013/04～2017/03	School of Informatics & Mathematical Science │ Faculty of Engineering │ Kyoto University │ Graduated

Business career
1.	2022/04/01 ～ 2024/03/31	Senior Researcher │ Research Organization of Science and Technology │ Ritsumeikan University
2.	2021/12 ～ 2022/03	│ │ Japan Society for the Promotion of Science
3.	2019/04 ～ 2021/11	│ │ Japan Society for the Promotion of Science

Subject of research
1.	Dynamical systems theory
2.	Hamiltonian systems
3.	Integrability and chaos

Research summary
Regular and chaotic motions of dynamical systems Shoya Motonaga is a researcher of dynamical systems. The study of Hamiltonian dynamical systems is a central subject of his research and he is working on extending such studies to non-Hamiltonian systems. In particular, his main interest is the various dynamics between the integrable cases and the chaotic cases. In his previous research, he has studied integrability criteria, which determine whether a given dynamical system is integrable or not, and analyzed the relationship between integrability (nonintegrability) and dynamics. It became widely known that ordinary differential equations are generally nonintegrable through Poincaré's study of restricted three-body problem, but it was not easy to determine whether a given ordinary differential equation or dynamical system is integrable or not. However, through the development of the Ziglin analysis and the Morales-Ramis theory for Hamiltonian systems, it has gradually become clear. Moreover, such studies are extended to non-Hamiltonian ones in recent years. He has been working on integrability determination of a given equation with the analysis of nonlinear oscillators such as forced Duffing oscillators in mind. In particular, he has been working on the question: is there a gap between non-integrability and chaos? He has been working on a new method of determining integrability from the viewpoint of conserved quantities and continuous symmetry, using differential Galois theory, perturbation theory, theory of manifolds, symplectic geometry, dynamical systems theory, etc. He has also investigated the connection with Melnikov analysis, which is one of the analytical methods for chaos. He is currently interested in various dynamics that are not limited to integrable or chaotic cases, and is investigating the possibility of generalizations of methods for Hamiltonian systems to non-Hamiltonian ones.

Present specialized field
Applied mathematics and statistics, Mathematical analysis, Geometry (Keyword：Hamiltonian systems)

Academic conference presentation
1.	2021/06	Obstructions to integrability of nearly integrable dynamical systems near regular level sets (RIMS研究集会「力学系理論の最近の進展とその応用」)
2.	2019/07	Nonpersistence of periodic orbits, homoclinic orbits, first integrals, and commutative vector fields in perturbed systems (Equadiff)
3.	2019/05	Nonpersistence of periodic orbits, homoclinic orbits, first integrals, and commutative vector fields in perturbed systems (International Conference on Finite Dimensional Integrable Systems in Geometry and Mathematical Physics)
4.	2018/12	Nonpersistence of periodic orbits, homoclinic orbits, first integrals and commutative vector fields in perturbed systems (Symmetry and Singularity of Geometric Structures and Differential Equations)
5.	2018/06	Nonintegrability of Parametrically Forced Nonlinear Oscillators (International Conference on Algebraic Methods in Dynamical Systems)

Works
1.	2020/06	Obstructions to the persistence and the existence of first integrals for nearly integrable systems

Message
1.	Toward a New Vision of Dynamical Systems Theory The fact that differential equations are in general not solved is explained in lectures of classical physics and differential equations without its proof usually. In order to show that quadrature is not possible, it is necessary to consider what it means that quadrature is possible, and what is the mechanism that prevents quadrature. If one tries to formulate quadrature in a coordinate-independent manner, geometrical aspects such as conserved quantities and continuous symmetry become important. If one wants to show nonintegrability, various perspectives are needed, for example, classical analysis, complex analytic and algebraic methods, and so on. It is said that Poincaré pioneered the field of dynamical systems by focusing on the behavior of solutions without being bound by the representation of solutions when he showed that the restricted three-body problem is nonintegrable, and it is also important to investigate the behavior of solutions regardless of whether they are solvable or not. For example, the very complicated behavior derived from a transversal intersection of stable and unstable manifolds is now known as a typical mechanism of chaos and is one of the main concepts of dynamical systems theory. Integrable dynamical systems and chaotic dynamical systems play a very important role in the study of dynamical systems theory, and I would like to connect them to new research by investigating the properties of dynamical systems one by one from these two viewpoints.