Perron Conditions for Uniform Exponential Expansiveness of Linear Skew-Product Flows

 We present necessary and sufficient conditions for uniform exponential expansiveness of discrete skew-product flows, in terms of uniform complete admissibility of the pair (c ₀(N, X), c ₀(N, X)). We give discrete and continuous characterizations for uniform exponential expansiveness of linear skew-product flows, using the uniform complete admissibility of the pairs (c ₀(N, X), c ₀(N, X)) and (C ₀(R ₊, X), C ₀(R ₊, X)), respectively. We generalize an expansiveness theorem due to Van Minh, R?biger and Schnaubelt, for the case of linear skew-product flows. Received August 10, 2001; in revised form June 25, 2002