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Nonlinear integral operators and chaos in Banach spaces

Published online by Cambridge University Press:  17 April 2009

Phil Diamond
Phil Diamond
Affiliation:
Mathematics Department, University of Queensland, St. Lucia, Queensland, Australia
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Abstract

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Sufficient conditions are given for chaotic behaviour of continuous transformations on Banach spaces. The conditions avoid the requirement that mappings be expanding on compact sets and are probably easier to verify for many classes of operator equations than existing criteria. Two classes of integral operators on C[0, 1] are considered in the light of these results: one nonlinear but compact, the second noncompact.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 2 , April 1987 , pp. 275 - 289
Copyright
Copyright © Australian Mathematical Society 1987

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