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Dynamical Systems Lab
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Dynamical systems is a field of research that uses mathematics to study mechanisms that change over time.
AboutAbout the lab
Capturing mechanisms that change over time through mathematics
A dynamical system is a mathematical formulation of rules that describe time evolution.
Typical examples are the equations of motion (ordinary differential equations) that describe the motion of celestial bodies and spinning tops. Dynamical systems also appear in many areas of physics and in models of chemical reactions, ecology, and economics.
Mathematical research itself also naturally defines many kinds of dynamical systems, and the goal of dynamical systems theory is to investigate their properties.
The faculty in this field specialize in dynamical systems as well as applied analysis and several complex variables, among other areas.
Key terms
- Dynamical system
- A description, in the language of mathematics, of rules by which a state changes over time.
- Ordinary differential equation
- An equation that describes how a quantity changes depending on a variable such as time. Equations of motion are an example.
- Oka principle
- A heuristic principle stating that analytic problems on Stein manifolds face only topological obstructions.
NewsLab news
Associate Professor Yuta Kusakabe received the Mathematical Society of Japan Spring Prize (FY2026)
Associate Professor Yuta Kusakabe received the Student Encouragement Award (Hida Prize) of the Nagoya University Mathematical Sciences Alumni Association
ResearchResearch themes
A dynamical system is a mathematical formulation of rules that describe time evolution. Dynamical systems theory aims to investigate the properties of dynamical systems using methods from real analysis, algebraic geometry, topology, complex analysis, probability theory, numerical computation, and more.
*Illustrative imageDynamical Systems Appearing in Many Fields
Dynamical systems appear widely, for example in the motion of celestial bodies and spinning tops and in models of chemical reactions, ecology, and economics. Many dynamical systems are also defined naturally within mathematics itself, and the lab studies their properties.
*Illustrative imageViewing Applied Analysis Through Geometry
Associate Professor Shunsaku Nii analyzes problems in applied analysis using dynamical systems theory, especially topological methods. By viewing problems that have traditionally been studied with analytic methods from a geometric angle, this work provides a new framework.
*Illustrative imageThe Oka Principle and Ellipticity in Complex Analysis
Associate Professor Yuta Kusakabe studies, within several complex variables and complex geometry, the Oka principle, a homotopy principle in complex analysis, and the area around "Gromov ellipticity," a property that is the exact opposite of Kobayashi hyperbolicity. The Oka principle is examined from a broader perspective that includes algebraic geometry and differential geometry.
MembersFaculty
- ProfessorYutaka Ishii
- ProfessorMasato Tsujii
- ProfessorKaname Matsue
- Associate ProfessorYuta Kusakabe
- Associate ProfessorShunsaku Nii
- Associate ProfessorYosuke Morita
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Lorenz caos3” António Miguel de Campos / Public domain (cropped)
- Dynamical Systems Appearing in Many Fields: “Pendulum” Antranias / CC0 (cropped)
- Viewing Applied Analysis Through Geometry: “ABA 3” MissLunaRose12 / CC BY-SA 4.0 (cropped)
- The Oka Principle and Ellipticity in Complex Analysis: “Complex Gamma Function” Naitronbomb / CC0 (cropped)
- Related lab (数理物理): “Crabbers eye knot-removebg-preview” Zaripov999 / CC BY-SA 4.0 (cropped)
- Related lab (微分方程式): “Gradient Vector Flow 3D Metasphere Example Result” YoungX2040 / CC BY-SA 4.0 (cropped)
- Related lab (トポロジー): “Klein bottle green” Aizenr / CC BY-SA 4.0 (cropped)
- Related lab (表現論・調和解析): “Worm's-eye view of Tokyo Skytree with vertical symmetry impression, a sunny day, in Japan” Basile Morin / CC BY-SA 4.0 (cropped)
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