University of Bremen - Analysishttps://www.uni-bremen.de/en/fb3/research/mathematics/research-profiles/analysisanalysis, mathematics, maths, topics, working groupsUniversity of BremenWed, 08 Feb 2023 05:17:59 +0100Wed, 08 Feb 2023 05:17:59 +0100University of Bremenhttps://www.uni-bremen.de/en/fb3/research/mathematics/research-profiles/analysis#c237812Working groups in Industrial Mathematics also utilise methods from Analysis. Contentcontent-237812Wed, 12 Feb 20 15:19:34 +0100https://www.uni-bremen.de/en/fb3/research/mathematics/research-profiles/analysis#c159628Contentcontent-159628Wed, 12 Feb 20 15:05:30 +0100https://www.uni-bremen.de/en/fb3/research/mathematics/research-profiles/analysis#c159631Contentcontent-159631Wed, 12 Feb 20 15:05:21 +0100https://www.uni-bremen.de/en/fb3/research/mathematics/research-profiles/analysis#c172259Contentcontent-172259Wed, 20 Mar 19 10:38:11 +0100https://www.uni-bremen.de/en/fb3/research/mathematics/research-profiles/analysis#c159633Within 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) Contentcontent-159633Mon, 02 Mar 20 14:40:31 +0100https://www.uni-bremen.de/en/fb3/research/mathematics/research-profiles/analysis#c237811Contentcontent-237811Wed, 12 Feb 20 15:12:33 +010060