Acta Physica Polonica B

Vol. 38, No. 5, May 2007, page 1909


Chaos in Newtonian Iterations: Searching for Zeros Which Are Not There

L. Skowronek, P.F. Gora

We show analytically that Newtonian iterations, when applied to a polynomial equation, have a positive topological entropy. In a specific example of an attempt to ``find'' the real solutions of the equation x2+1=0, we show that the Newton method is chaotic. We analytically find the invariant density and show how this problem relates to that of a piecewise linear map.

PACS numbers: 05.45.--a



 
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