Hilbert Space Embeddings in Dynamical Systems

Dilations for $C^ast$-dynamical systems with abelian groups on Hilbert $C^ast$-modules

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...

Dynamical Systems on Hilbert C*-Modules

Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces

Transfer operators such as the Perron–Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The eigenfunctions of these operators can be used to detect metastable sets, to project the dynamics onto the dominant slow processes, or to separate superimposed signals. We extend transfer operator theory to reproducing kernel Hilbert spaces and show ...

Dynamical distance as a semi-metric on nuclear conguration space

In this paper, we introduce the concept of dynamical distance on a nuclear conguration space. We partition the nuclear conguration space into disjoint classes. This classification coincides with the classical partitioning of molecular systems via the concept of conjugacy of dynamical systems. It gives a quantitative criterion to distinguish dierent molecular structures.

A hypothesis concerning “quantal” Hilbert space criterion of chaos in nonlinear dynamical systems

Based on the Hilbert space approach to the theory of nonlinear dynamical systems developed by the author a hypothesis is formulated concerning the " quantal " criterion for classical ordinary differential systems to exhibit chaotic behaviour.