Introducing isodynamic points for binary forms and their ratios

@article{Hgg2022IntroducingIP,
  title={Introducing isodynamic points for binary forms and their ratios},
  author={Christian H{\"a}gg and Boris Z. Shapiro and Michael Shapiro},
  journal={Complex Analysis and its Synergies},
  year={2022},
  volume={9}
}
The isodynamic points of a plane triangle are known to be the only pair of its centers invariant under the action of the Möbius group M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {M}}$$\end{document} on the set of triangles, Kimberling (Encyclopedia of Triangle Centers, http://faculty.evansville.edu… 

References

SHOWING 1-10 OF 18 REFERENCES

Rodrigues' descendants of a polynomial and Boutroux curves

Motivated by the classical Rodrigues’ formula, we study below the root asymptotic of the polynomial sequence R[αn],n,P (z) = d[αn]Pn(z) dz[αn] , n = 0, 1, . . . where P (z) is a fixed univariate

Graphs on Surfaces and Their Applications

0 Introduction: What is This Book About.- 1 Constellations, Coverings, and Maps.- 2 Dessins d'Enfants.- 3 Introduction to the Matrix Integrals Method.- 4 Geometry of Moduli Spaces of Complex Curves.-

Classifying real polynomial pencils

We identify ℝℙ n with the space of real homogeneous polynomials of degree n in two variables considered up to a scalar factor. The standard discriminant Dn+1⊂ℝℙn is Whitney-stratified according to

Catalog of Properties of the First Isodynamic Point of a Triangle

Geometrical definition. The interior and exterior angle bisectors of angle A of 4ABC intersects side BC of the triangle (or its extension) in two points, A1 and A2. The circle with diameter A1A2 is

Discriminants, Resultants, and Multidimensional Determinants

Preface.- Introduction.- General Discriminants and Resultants.- Projective Dual Varieties and General Discriminants.- The Cayley Method of Studying Discriminants.- Associated Varieties and General

Duality between loci of complex polynomials and the zeros of polar derivatives

Abstract This work investigates the connections between the notion of a locus of a complex polynomial and the polar derivatives. Polar differentiation extends classical derivatives and provides

Geometry of Polynomials

During the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality

Inequalities for real-root polynomials and entire functions

GENERALIZATIONS OF NEWTON'S METHOD

We give a survey of the complex dynamics of various generalizations of Newton's method for finding a complex root of a polynomial of a single variable.

Encyclopedia of Triangle Centers

  • http://faculty. evansville.edu/ck6/encyclopedia. Accessed
  • 2022