Singular perturbations arising in complex Newton's method

Abstract

We examine the resulting dynamics when Newton's method is applied to perturbations on polynomials that have a multiple root. Specifically, we consider the case where Newton's method is applied to the polynomial family $(z^2 + c)(z-1).$

Keywords

• Julia set
• Newton method
• rational iteration
• singular perturbations

Supporting Institution

TUBİTAK

References

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