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Adam Epstein | Warwick University - Inglaterra

Grant number: 16/50432-2
Support type:Research Grants - Visiting Researcher Grant - International
Duration: July 15, 2019 - August 15, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Cooperation agreement: Newton Fund, with FAPESP as a partner institution in Brazil
Principal researcher:Luciana Luna Anna Lomonaco
Grantee:Luciana Luna Anna Lomonaco
Visiting researcher: Adam Epstein
Visiting researcher institution: University of Warwick, England
Principal researcher abroad: Shaun Bullet
Institution abroad: Queen Mary University of London, England
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The moduli space of cubic polynomials with labelled critical points is canonically isomorphic to CZ, via the normal form F _{a,b}(x)=z3-3a2z+b. The corresponding connectedness locus K seems (by computer experimentation of Milnor) to contain various structures apparently homeomorphic to products of limbs of the Mandelbrot set M. Work of Epstein and Yampolsky established this rigorously by means of quasiconformal surgery. However, for serious technical reasons, their arguments do not apply at persistently parabolic parameters. During the visit of A. Epstein we plan to apply the theory of parabolic-Iike mappings, developed in the host researcher's PhD thesis, to address the missing case. (AU)

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