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Myrberg, Pekka    

Pekka Juhana Myrberg (1892-1976) was a Finnish mathematician who studied the quadratic iteration z -> 1 + c z2 which is mostly equivalent to the Mandelbrot set iteration (see _Myrberg polynomials). He was the first to give a numerical value for the value of c at the limit of the period doubling bifurcation, commonly called the Feigenbaum point. The value -1.401155 appears on page 344 in the 1962 article Sur l'itération des polynomes quadratiques [PM1]:

From Myrberg's 1962 paper
From Myrberg's 1962 paper

and the exact location of the nucleus of the period-3 minibrot is in his 1963 article Iteration der reellen Polynome zweiten Grades III [PM2]:

From Myrberg's 1963 paper
From Myrberg's 1963 paper

This 1963 paper also shows the locations (almost certainly computed numerically) for the two period-4 nuclei on the real axis.

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.

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