V.A. Pliss, G.R. Sell, Robustness of exponential dichotomies in infinite--dimensional dynamical systems, J. Dynam. Differential Equations 11 (1999), 471--514.  Home/Search   Document Details and Download   Summary   Related Articles

....R and R Gamma play an important role in dynamical systems, cf. 79] 89] and the references therein. We mention three more characterizations of hyperbolicity. First, one can replace in the equivalence (a) b) of Theorem 5. 2 function spaces on R by sequence spaces over Z, see [26] 55, x7.6] [110], and [11] 25] 73] 74] where this approach is used in the context of evolution semigroups. Sequence spaces over N are considered in [10] 16] For X = C it is known that exponential dichotomy is equivalent to the existence of a bounded, continuously differentiable Hermitian matrix ....

....the evolution semigroup from the easier accessible results for semigroups. A third characterization of exponential dichotomy involves the hull A of the operators A(s) i.e. the closure of the translates R 3 7 A(t ) t 2 R, in an appropriate metric space, see [25] 26] 27] 28] 78] [110], 121] and the references therein. This approach requires, besides the existence of A, certain compactness and almost periodicity properties. Then one obtains that the evolution family generated by A( Delta) is hyperbolic if the equations u (t) B(t)u(t) t 2 R, do not admit a nontrivial ....

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V.A. Pliss, G.R. Sell, Robustness of exponential dichotomies in infinite--dimensional dynamical systems, J. Dynam. Differential Equations 11 (1999), 471--514.

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