Publication:
Chaos on function spaces

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Publication Date
2005
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Cambridge University Press
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We give a sufficient condition for an operator to be chaotic and we use this condition to show that, in the Banach space C-0[0, infinity) the operator (T(lambda,c)f) (t) = lambda f (t + c) (with lambda > 1 and c > 0) is chaotic, with every n is an element of N being a period for this operator. We also describe a technique to construct, explicitly, hypercyclic functions for this operator.
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J. Banks, J. Brooks, G. Cairns, G. Davies, and P.Stacey, 'On Devaney's definition of chaos', Amer. Math. Monthly 99 (1992), 332-334. R..L. Devaney, An introduction to chaotic dynamical systems, (Second Edition) (Addison-Wesley Publishing Company Inc., 1989). W. Desch, W. Schappacher, and G.F. Webb, 'Hypercyclic and chaotic semigroups of linear operators', Ergodic Theory Dynamical Systems 17 (1997), 793-819. K.-G. Grosse-Erdmann, 'Universal families and hypercyclic operators', Bui Amer. Math.Soc. 36 (1999), 345-381. C. Kitai, Invariant closed sets for linear operators,(Ph.D. Thesis) (University of Toronto,Toronto, Canada, 1982). A. Weber, Chaotic semigroups, (Diplomarbeit, in German)(Universitat Karlsruhe, 2002).
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