Lie group valued Koopman eigenfunctions

Abstract Every continuous-time flow on a topological space has associated to it Koopman operator, which operates by time-shifts various spaces of functions, such as C r , L 2 or functions bounded variation. An eigenfunction the vector field (and thus for operator) can be viewed an S 1 -valued function, also plays role semiconjugacy rigid rotation . This notion eigenfunctions will generalized Lie-group valued eigenfunctions, and we discuss dynamical aspects these functions. One tools that developed aid discussion, is concept exterior derivative Lie group generalizes differential d f real function f The extended utilizes geometric property usual eigenfunctions. We show generalization in sense used reveal fundamental properties their behaviour under time-rescaling, submersions.