Ergodic Theory and Dynamical Systems

Chaos for functions of discrete and continuous weighted shift operators

a1 Scientia Research Institute, 22000 Jordan Run Road, Guysville, Ohio 45735, USA (e-mail:
a2 Université de Poitiers, Laboratoire de Modélisation Mécanique et de Mathématiques Appliquées, SP2MI, BP 30179, F 86962 Futuroscope Cedex, France (e-mail:


For L equal to the unilateral or bilateral shift on a weighted sequence space, we characterize, in terms of f and the weight function, those f holomorphic on the spectrum of L for which f(L) is a chaotic operator. For B equal to d/dx, the generator of left translation, on weighted L^p spaces on [0, \infty) or \mathbb{R}, we similarly characterize those polynomials Q for which the differential operator Q(B) generates a chaotic semigroup.

(Received January 5 2000)
(Revised September 20 2000)