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Mathematical Sciences

Mathematical Sciences Research

Applied Geometry
Approximation Theory
Chemically-Reacting Flows
Computational Logic
Dynamical Systems
Environmental Problems
Fluid Dynamics
Inverse Problems
Machine Learning
Math Education
Mathematical Physics
Multiphase Flows
Nonlinear Analysis
Nonlinear Materials
Nonlinear Waves
Operations Research and Mathematical Programming
Perturbation Methods
Scientific Computing

Mathematical Sciences Research
Dynamical Systems

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:

  • Mechanics.
  • Optics.
  • 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:

  • Analysis.
  • Topology.
  • Differential geometry.
  • Combinatorics.

Researchers may use computation as an experimental tool.

Current Projects

Researchers conduct theoretical study of:

  • Chaotic dynamics.
  • Hamiltonian systems.
  • KAM theory and applications.
  • Theoretical mechanics.
  • Bifurcation theory.

Faculty Researchers

Gregor Kovacic
Chjan Lim
Yuri Lvov


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