• Corpus ID: 220280957

A theoretical framework for Koopman analyses of fluid flows, part 1: local Koopman spectrum and properties.

  title={A theoretical framework for Koopman analyses of fluid flows, part 1: local Koopman spectrum and properties.},
  author={Wei Zhang and Mingjun Wei},
  journal={arXiv: Fluid Dynamics},
Local Koopman spectral problem is studied to resolve all dynamics for a nonlinear system. The proposed spectral problem is compatible with the linear spectral theory for various linear systems, and several properties of local Koopman spectrums are discovered. Firstly, proliferation rule is discovered for nonlinear observables and it applies to nonlinear systems recursively. Secondly, the hierarchy structure of Koopman eigenspace of nonlinear dynamics is revealed since dynamics can be decomposed… 
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