A dynamical system is a deterministic process in which a function's value changes over time according to a rule that is defined in terms of the function's current value.
Dynamical systems arise as mathematical models in various applications such as:
- Electric circuits.
- Solid-state physics.
- Fluid dynamics.
- Optimal control.
- Neural science.
Researchers often model real-life problems with a dynamical system and then apply the ideas and methods of the theory to explain and predict complex behavior.
Dynamical Systems at Rensselaer
Researchers at Rensselaer concentrate on the theory of dynamical systems and its applications in physics and engineering.
This research aims to discover and explain new and important phenomena found in experimental and numerical studies.
The mathematical methods used come from:
- Differential geometry.
Researchers may use computation as an experimental tool.
Researchers conduct theoretical study of:
- Chaotic dynamics.
- Hamiltonian systems.
- KAM theory and applications.
- Theoretical mechanics.
- Bifurcation theory.