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- W1529656148 abstract "The Daleckij-Krein method for constructing a quadratic Lyapunov function for the equation $f'=Df(t)$ in Hilbert space is extended to include the case of an unbounded operator $D$ that generates a $C_0$-group. The extension is applied to obtain a quadratic Lyapunov function for the case of a group of weighted composition operators generated by a flow on a compact metric space together with a cocycle over this flow. These results are used to characterize the hyperbolicity of linear skew-product flows in terms of the existence of such a Lyapunov function. Also, the trajectorial method for constructing the Lyapunov function is discussed. Interrelations with Schrödinger, Riccati and Hamiltonian equations are discussed and an application to geodesic flows on two-dimensional Riemannian manifolds is given." @default.
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- W1529656148 date "1995-01-01" @default.
- W1529656148 modified "2023-10-16" @default.
- W1529656148 title "Quadratic Lyapunov functions for linear skew-product flows and weighted composition operators" @default.
- W1529656148 doi "https://doi.org/10.57262/die/1369083470" @default.
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