CHAOS FOR BACKWARD SHIFT OPERATORS
2002 ◽
Vol 12
(08)
◽
pp. 1703-1715
◽
Keyword(s):
Backward shift operators provide a general class of linear dynamical systems on infinite dimensional spaces. Despite linearity, chaos is a phenomenon that occurs within this context. In this paper we give characterizations for chaos in the sense of Auslander and Yorke [1980] and in the sense of Devaney [1989] of weighted backward shift operators and perturbations of the identity by backward shifts on a wide class of sequence spaces. We cover and unify a rich variety of known examples in different branches of applied mathematics. Moreover, we give new examples of chaotic backward shift operators. In particular we prove that the differential operator I + D is Auslander–Yorke chaotic on the most usual spaces of analytic functions.
1999 ◽
Vol 9
(2)
◽
pp. 197-211
◽
2019 ◽
Vol 29
(12)
◽
pp. 1950170
1977 ◽
1998 ◽
Vol 08
(PR6)
◽
pp. Pr6-227-Pr6-231
Comparison of the methods of parametric identification of linear dynamical systems under mixed noise
2018 ◽
Vol 18
(3)
◽
pp. 45-59