Preprint No. A-99-21

Wolf Bayer, Rudolf Gorenflo

Devaney chaos by iterated differentiation of analytical functions

Abstract: By checking the relevant conditions we prove that the common operator of differentiation, acting in a suitable metricized space of analytic functions, is chaotic in the sense of Devaney even though it is a linear operator. To invalidate the possible objection that in view of this operator's discontinuity there is nothing to wonder about we show by an example that discontinuity of a mapping and sensitivity are independent.

Keywords: chaos, differential operator, hyperbolic functions, butterfly-effect

Mathematics Subject Classification (MSC91): 58-XX, Global analysis, analysis on manifolds ; 47-XX Operator theory

Language: ENG

Available: Pr-A-99-21.ps

Contact: Gorenflo, Rudolf, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (gorenflo@math.fu-berlin.de)

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