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)