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Analysis

Within the research focus group Analysis, there are diverse research areas pertaining to dynamical systems. In the broadest sense dynamical systems means the investigation of mathematical structures with a time-like variable. Within dynamical systems, a distinction is made between continuous time, which leads to differential equations, and discrete time, which occurs during the iteration procedure. The theory of dynamical systems can be applied within the mathematical fields of number theory, measure and probability theory, and differential equations. Applications outside of mathematics can be found in climate research, geophysics, ecology, neurobiology, and fluid mechanics. 

The topics of the groups within the research focus group Analysis include the following:

Dynamical Systems and Geometry

  • Ergodic theory (Pohl, Keßeböhmer)
  • Hyperbolic geometry and homogeneous spaces (Keßeböhmer, Pohl)
  • Fractal geometry (Keßeböhmer)
  • Quantum chaos (Pohl)
  • Ordinary and partial differential equations (Rademacher, Vogt)
  • Branches, pattern formation, non-linear waves and stability (Rademacher)
  • Applications in geophysics, ecology, fluid mechanics, control engineering (Rademacher)

Harmonic Analysis

  • Harmonic analysis on fractals (Keßeböhmer)
  • Spectral theory of symmetric spaces (Pohl)

Functional Analysis

  • Operator theory (Vogt)
  • Non-linear partial differential equations, differential equations (Rademacher, Vogt)
  • Spectral theory (Keßeböhmer, Pohl, Rademacher, Vogt)
  • Transfer and Laplace operators (Keßeböhmer, Pohl)

Number Theory

  • Analytic number theory (Pohl)
  • Metric number theory (Keßeböhmer)

Involved Working Groups

Working groups in Industrial Mathematics also utilise methods from Analysis.