Zeitschrift für Analysis und ihre Anwendungen
Full-Text PDF (988 KB) | Metadata | Table of Contents | ZAA summary
Published online: 1996-12-31
Hyperbolic Linear Skew-Product SemiflowsR.T. Rau (1) Universität Tübingen, Germany
A spectral theory for evolution operators on Banach spaces has been developed in [14, 15] considering associated $C_0$-semigroups on vector-valued function spaces. It is then quite natural to substitute the shift on $\mathbb R$ by an arbitrary flow $\sigma$ on a topological space $X$ and to substitute the evolution operator by a cocycle $\Phi$ over $\sigma$. This task was performed by Latushkin and Stepin (cf. [8, 9]) for hyperbolic linear skew-product flows assuming some norm continuity of this flow. In general only strong continuity can be obtained (cf. Sacker and Sell [18) and Example 2 below). Following a suggestion by Hale [7: p. 601 we consider strongly continuous linear skew-product flows in Banach spaces and characterize hyperbolicity through a spectral condition.
Keywords: $C_0$-semi groups, cocycles, exponential dichotomy, skew-product flows
Rau R.T.: Hyperbolic Linear Skew-Product Semiflows. Z. Anal. Anwend. 15 (1996), 865-880. doi: 10.4171/ZAA/734