This book presents the development and application of some topological methods in the analysis of data coming from 3D dynamical systems (or related objects). The aim is to emphasize the scope and limitations of the methods, what they provide and what they do not provide. Braid theory, the topology of surface homeomorphisms, data analysis and the reconstruction of phase-space dynamics are thoroughly addressed.
- A Crisis in the Experimental Method Archetype
- Orbit Organization in R2 x S1
- Braids as Indicators of Phase-Space Dynamics
- Braids and the Poincaré Section
- Reconstruction of Phase-Space Dynamics — Basic Course
- Reconstruction of Phase-Space Dynamics — Advanced Course
Readership: Researchers in geometry and topology and mathematical modeling.