Koopman and Transfer Operators
Operator-theoretic approach to dynamics and dynamic mode decomposition.
Koopman and Transfer Operators. Operator-theoretic approach to dynamics and dynamic mode decomposition.
Foundations and canonical references
The standard treatments of koopman and transfer operators approach the subject from complementary angles. Budisic, Applied Koopmanism (2012) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Kutz, Dynamic Mode Decomposition (2016) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for koopman and transfer operators include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2012Applied Koopmanismbudisic-2012, mohr-2012, mezic-2012
- textbook · primary · 2016Dynamic Mode Decompositionkutz-2016, brunton-2016, brunton-bingni-2016, proctor-2016
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