Hilbert space description of nonlinear discrete-time dynamical systems
The author shows that very general nonlinear recurrences of the form \(x_{n + 1} = f(x_ n)\) where \(f\) is analytic in \(x_ n\) may be cast into the linear abstract recurrence in Hilbert space with the displacement operator expressed in terms of Bose creation and annihilation operators. This generalizes the Carleman linearization approach that corresponds to the particular occupation number representation [see the author and \textit{W.-H. Steeb}, `Nonlinear dynamical systems and Carleman linearization' (1991; Zbl 0753.34003) and \textit{W.-H. Steeb}, in `Nonlinear phenomena in chemical dynamics' (1991)]. The formalism introduced in the paper is applied to the study of the linearization transformations for nonlinear difference equations and Feigenbaum-Cvitanovic renormalization equations.
Feigenbaum- Cvitanovic renormalization equations
scientific article; zbMATH DE number 606944