Displaying similar documents to “From Newton's method to exotic basins Part II: Bifurcation of the Mandelbrot-like sets”

Invertible polynomial mappings via Newton non-degeneracy

Ying Chen, Luis Renato G. Dias, Kiyoshi Takeuchi, Mihai Tibăr (2014)

Annales de l’institut Fourier

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We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.

Branched coverings and cubic Newton maps

Lei Tan (1997)

Fundamenta Mathematicae

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We construct branched coverings such as matings and captures to describe the dynamics of every critically finite cubic Newton map. This gives a combinatorial model of the set of cubic Newton maps as the gluing of a subset of cubic polynomials with a part of the filled Julia set of a specific polynomial (Figure 1).

A global analysis of Newton iterations for determining turning points

Vladimír Janovský, Viktor Seige (1993)

Applications of Mathematics

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The global convergence of a direct method for determining turning (limit) points of a parameter-dependent mapping is analysed. It is assumed that the relevant extended system has a singular root for a special parameter value. The singular root is clasified as a b i f u r c a t i o n s i n g u l a r i t y (i.e., as a d e g e n e r a t e turning point). Then, the Theorz for Imperfect Bifurcation offers a particular scenario for the split of the singular root into a finite number of regular roots (turning points) due to a given parameter imperfection....