Advances in Dynamical Systems and Applications
  • Year: 2006
  • Volume: 1
  • Issue: 2

Exponential Expansiveness and Variational Integral Equations

  • Author:
  • Bogdan Sasu
  • Total Page Count: 8
  • Page Number: 191 to 198

Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timis¸oara, Parvan Blv. No. 4, 300223Timis¸oara, Romania. E-mail: bsasu@math.uvt.ro

AMS subject classification: 47D06, 34D05, 34G99.

Abstract

We associate with a linear skewproduct flow π = (Φ,σ) a variational integral equation and we characterize the exponential expansiveness of π in terms of the solvability of the associated equation. We prove that a linear skewproduct flow on X×θ is uniformly exponentially expansive if and only if the pair (V(ℝ+,X),Cc(ℝ+,X)) is uniformly exactly admissible for π, where V(ℝ+,X) denotes one of the spaces C0(ℝ+,X) or Cb(ℝ+,X).

Keywords

Linear skewproduct flow, exponentially expansive