Chaos in Newtonian iterations: Searching for zeros which are not there
Lukasz Skowronek, P. F. Gora
Abstract
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.
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