研究紹介
キーワード
1. Invariant manifolds (e.g., stable/unstable manifolds of hyperbolic fixed points and Normally Hyperbolic Invariant Manifolds, NHIMs) in chaotic systems, and their applications to chemical reaction dynamics;, 2. The topology and geometry of four-dimensional chaotic maps;, 3. Mathematical modeling in meteorology.
研究概要
Nonlinear dynamical systems and chaos theory provide a panoptic framework across scientific disciplines. Whether it is molecular predissociation, a spacecraft navigating the gravitational fields of the Sun, Earth, and Jupiter, or large-scale atmospheric motion in weather forecasting and numerical meteorology, many systems exhibit extreme sensitivity to initial conditions and environmental perturbations. Although these phenomena look very different, their governing equations often share common geometric structures—the focus of nonlinear dynamics and chaos theory.
代表的な研究成果
- K. Fujioka, R. Kogawa, J. Li, and A. Shudo, “Topological horseshoe and uniform hyperbolicity of the symplectic coupled Hénon map,” Physica D: Nonlinear Phenomena 481, 134722 (2025).
- L. Li, J. Li, and T. Miyoshi, “Chaos suppression through chaos enhancement,” Nonlinear Dynamics (2024), Editor’s Choice.
- J. Li and S. Tomsovic, “Homoclinic orbit expansion of arbitrary trajectories in chaotic systems: classical action function and its memory,” arXiv:2009.12224 [nlin.CD] (2020).
- J. Li and S. Tomsovic, “Asymptotic relationship between homoclinic points and periodic orbit stability exponents,” Phys. Rev. E 100, 052202 (2019).
- J. Li and S. Tomsovic, “Exact relations between homoclinic and periodic orbit actions in chaotic systems,” Phys. Rev. E 97, 022216 (2018).