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Horenkamp, Christian: Efficient detection of coherent structures in non-autonomous dynamical systems via transfer operator methods. 2014
Inhalt
Introduction
Dynamical System Theory - Basic Concepts
Autonomous Dynamical Systems
Non-Autonomous Dynamical Systems
Ergodic Theory
Transfer Operators
Transport in Dynamical Systems
Coherence Ratio
Autonomous Coherent Structures
Invariant Sets
Almost Invariant Sets
Non-Autonomous Coherent Structures
Coherent Pairs
Analysis of Transport over Long Time Intervals
Product Approach
Error Estimate
Algorithmic Realization
Efficient Numerical Approximation of Coherent Structures
Connecting Almost Invariant Sets and Coherent Pairs
Algorithm for the Efficient Approximation of Coherent Pairs
Numerical Effort
Example
Parameter Adaption
Detection of Coherent Structures in the Ocean
Transfer Operator Methods for the Oceanic Fluid Flow
Seasonal Variability of the Subpolar Gyres in the Southern Ocean
Water Flux of the Subpolar Gyres
Mean Residence Time
Pathway of Water
Three-dimensional Characterization and Tracking of an Agulhas Ring
Domain Preselection
Application of the Product Approach
Comparison with Other Techniques
Conclusion
List of Figures
Bibliography
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