Topological models in holomorphic dynamics

• Grant number: 11/12650-4
• Support type: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): November 01, 2011
• Effective date (End): October 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal researcher: André Salles de Carvalho
• Grantee: Sylvain Philippe Pierre Bonnot
• Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project has the purpose to build topological models for holomorphic dynamical systems. The first part will study topological ramified covering maps of the sphere up to isotopy, by reducing them to one-dimensional graphs ("train tracks") carrying all the relevant dynamical information.The second part will be devoted to complex Henon maps and will provide topological models by pinching four dimensional balls along dynamically defined laminations on the boundary.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BONNOT, S.; DE CARVALHO, A.; MESSAOUDI, A. Julia sets for Fibonacci endomorphisms of (2). DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 33, n. 4, p. 622-645, 2018. Web of Science Citations: 1.