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A Classification of Postcritically Finite Newton Maps

In: In the Tradition of Thurston II

Author

Listed:
  • Russell Lodge

    (Indiana State University, Department of Mathematics and Computer Science)

  • Yauhen Mikulich

  • Dierk Schleicher

    (UMR 7373, Institut de Mathématiques de Marseille, Aix-Marseille Université and CNRS)

Abstract

The dynamical classification of rational maps is a central concern of holomorphic dynamics. Much progress has been made, especially on the classification of polynomials and some approachable one-parameter families of rational maps; the goal of finding a classification of general rational maps is so far elusive. Newton maps (rational maps that arise when applying Newton’s method to a polynomial) form a most natural family to be studied from the dynamical perspective. Using Thurston’s characterization and rigidity theorem, a complete combinatorial classification of postcritically finite Newton maps is given in terms of a finite connected graph satisfying certain explicit conditions.

Suggested Citation

  • Russell Lodge & Yauhen Mikulich & Dierk Schleicher, 2022. "A Classification of Postcritically Finite Newton Maps," Springer Books, in: Ken’ichi Ohshika & Athanase Papadopoulos (ed.), In the Tradition of Thurston II, chapter 0, pages 421-448, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-97560-9_13
    DOI: 10.1007/978-3-030-97560-9_13
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