Bulletin of the Australian Mathematical Society

Research Article

Chaos on function spaces

Richard M. Arona1, Juan B. Seoane-Sepúlvedaa1 and Andreas Webera2

a1 Math Department, Kent State University, Kent, Ohio, 44242, United States of America, e-mail: aron@math.kent.edu, jseoane@math.kent.edu

a2 Mathematisches Institut II, Universität Karlsruhe, D-76128 Karlsruhe, Germany, e-mail: andreas.weber@math.uni-karlsruhe.de

We give a sufficient condition for an operator to be chaotic and we use this condition to show that, in the Banach space C0[0, ∞) the operator (τλ, cf)(t) = λf(t + c) (with λ > 1 and c > 0) is chaotic, with every n xs2208 xs2115 being a period for this operator. We also describe a technique to construct, explicitly, hypercyclic functions for this operator.

(Received December 01 2004)