Naslov
Smooth Linearization of Nonautonomous Coupled Systems

Autori
Backes, Lucas ; Dragičević, Davor

Izvornik
Discrete and continuous dynamical systems-series b (1531-3492) 28 (2023), 8; 4497-4518

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
linearization ; differentiability ; nonautonomous coupled systems

Sažetak
In a joint work with Palmer \cite{; ; BDP}; ; we have formulated sufficient conditions under which there exist continuous and invertible transformations of the form $H_n(x, y)$ taking solutions of a coupled system \begin{; ; equation*}; ; x_{; ; n+1}; ; =A_nx_n+f_n(x_n, y_n), \quad y_{; ; n+1}; ; =g_n( y_n), \end{; ; equation*}; ; onto the solutions of the associated partially linearized uncoupled system \begin{; ; equation*}; ; x_{; ; n+1}; ; =A_nx_n, \quad y_{; ; n+1}; ; =g_n( y_n). \end{; ; equation*}; ; In the present work we go one step further and provide conditions under which $H_n$ and $H_n^{; ; -1}; ; $ are smooth in one of the variables $x$ and $y$. We emphasise that our conditions are of a general form and do not involve any kind of dichotomy, nonresonance or spectral gap assumptions for the linear part which are present on most of the related works.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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