Chaos in Newtonian iterations: Searching for zeros which are not there

Details Chaos in Newtonian iterations: Searching for zeros which are not there Chaos in Newtonian iterations: Searching for zeros which are not there

2007-03-29

arxiv.org/abs/nlin/0703061v1

Acta Physica Polonica B 38(5), 1909 (2007)

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

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 $x^2+1=0$, 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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