コロキウム

The Koopman operators are widely used in applications of dynamical systems theory to data science. In this talk, we mainly consider linear systems whose coefficient matrices are in Jordan normal form, and discuss eigenvalue problems of the Koopman and Lie operators. I first state definitions and basic results of the Koopman and Lie operators, and introduce the Hartman-Grobman theorem and Zung's result on Poincare-Dulac normal forms. I present a theorem on eigenvalues and generalized eigenfunctions of the operators, and two corollaries following from the Hartman-Grobman theorem and Zung's result for nonlinear systems. Finally, I state the plan for my graduation research in the remaining period.