DYNAMICS OF SCHWARZ REFLECTIONS: THE MATING PHENOMENA

Seung Yeop Lee; Mikhail Lyubich; Nikolai G. Makarov; Sabyasachi Mukherjee

doi:10.24033/asens.2568

DYNAMICS OF SCHWARZ REFLECTIONS: THE MATING PHENOMENA

Seung Yeop Lee
, Mikhail Lyubich
, Nikolai G. Makarov
, Sabyasachi Mukherjee

Mathematical Science Institute

University of South Florida
California Institute of Technology
Tata Institute of Fundamental Research

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We initiate the exploration of a new class of anti-holomorphic dynamical systems generated by Schwarz reflection maps associated with quadrature domains. More precisely, we study Schwarz reflection with respect to the deltoid, and Schwarz reflections with respect to the cardioid and a family of circumscribing circles.We describe the dynamical planes of the maps in question, and show that in many cases, they arise as unique conformal matings of quadratic anti-holomorphic polynomials and the ideal triangle group.

Original language	English
Pages (from-to)	1825-1881
Number of pages	57
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	56
Issue number	6
DOIs	https://doi.org/10.24033/asens.2568
State	Published - 2023

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10.24033/asens.2568

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abstract = "We initiate the exploration of a new class of anti-holomorphic dynamical systems generated by Schwarz reflection maps associated with quadrature domains. More precisely, we study Schwarz reflection with respect to the deltoid, and Schwarz reflections with respect to the cardioid and a family of circumscribing circles.We describe the dynamical planes of the maps in question, and show that in many cases, they arise as unique conformal matings of quadratic anti-holomorphic polynomials and the ideal triangle group.",

author = "Lee, \{Seung Yeop\} and Mikhail Lyubich and Makarov, \{Nikolai G.\} and Sabyasachi Mukherjee",

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AU - Lee, Seung Yeop

AU - Lyubich, Mikhail

AU - Makarov, Nikolai G.

AU - Mukherjee, Sabyasachi

PY - 2023

Y1 - 2023

N2 - We initiate the exploration of a new class of anti-holomorphic dynamical systems generated by Schwarz reflection maps associated with quadrature domains. More precisely, we study Schwarz reflection with respect to the deltoid, and Schwarz reflections with respect to the cardioid and a family of circumscribing circles.We describe the dynamical planes of the maps in question, and show that in many cases, they arise as unique conformal matings of quadratic anti-holomorphic polynomials and the ideal triangle group.

AB - We initiate the exploration of a new class of anti-holomorphic dynamical systems generated by Schwarz reflection maps associated with quadrature domains. More precisely, we study Schwarz reflection with respect to the deltoid, and Schwarz reflections with respect to the cardioid and a family of circumscribing circles.We describe the dynamical planes of the maps in question, and show that in many cases, they arise as unique conformal matings of quadratic anti-holomorphic polynomials and the ideal triangle group.

UR - https://www.scopus.com/pages/publications/85188776498

U2 - 10.24033/asens.2568

DO - 10.24033/asens.2568

M3 - Article

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SN - 0012-9593

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JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

IS - 6

ER -

DYNAMICS OF SCHWARZ REFLECTIONS: THE MATING PHENOMENA

Abstract

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