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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