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Chaos on function spaces

Published online by Cambridge University Press:  17 April 2009

Richard M. Aron ,
Juan B. Seoane-Sepúlveda  and
Andreas Weber
Richard M. Aron
Affiliation:
Math Department, Kent State University, Kent, Ohio, 44242, United States of America, e-mail: [email protected], [email protected]
Juan B. Seoane-Sepúlveda
Affiliation:
Math Department, Kent State University, Kent, Ohio, 44242, United States of America, e-mail: [email protected], [email protected]
Andreas Weber
Affiliation:
Mathematisches Institut II, Universität Karlsruhe, D-76128 Karlsruhe, Germany, e-mail: [email protected]
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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 C0[0, ∞) the operator (τλ, cf)(t) = λf(t + c) (with λ > 1 and c > 0) is chaotic, with every n ∈ ℕ being a period for this operator. We also describe a technique to construct, explicitly, hypercyclic functions for this operator.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 3 , June 2005 , pp. 411 - 415
Copyright
Copyright © Australian Mathematical Society 2005

References

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