Summary
International Symposium on Nonlinear Theory and Its Applications
2016
Session Number:B2L-B
Session:
Number:B2L-B-6
A Schrodinger-Type Formalism and Observable Wavefunctions in Dynamical Systems
Igor Mezi?,
pp.-
Publication Date:2016/11/27
Online ISSN:2188-5079
Summary:
There is recent interest in the use of Koopman (composition) operator theory for a wide range of problems in dynamical systems. In its dual, Perron-Frobenius theory, the use of invariant measures for understanding of statistical properties of dynamical systems is routine. A much less used concept is that of eigenmeasures. We extend the theory related to eigenmeasures to introduce the notion of wavefunctions into dynamical systems theory. A wavefunction can be thought of as the density of a complex measure on the state space. It satisfies the common Perron-Frobenius equation. Using this, we derive a Schrodinger-type formalism for complex measure propagation on embeddings of dynamical system dynamics into the output space of an observable propagated by the Koopman operator. The resulting wavefunction is named an observable wavefunction (OW).