Singular perturbations of rational maps

• Grant number: 11/00028-7
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: May 25, 2011
• End date: June 11, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Edson Vargas
• Grantee: Edson Vargas
• Visiting researcher: Robert Devaney
• Visiting researcher institution: Boston University (BU), United States
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project contains two parts: the first part is a mini-course with 6 talks about dynamics of rational functions on the Riemann sphere (singular perturbations, mainly) and entire functions on the complex plane. Topological, ergodic and metrical aspects will be treated. The second part is a research about singular perturbations of rational functions, more precisely we are interested on the topological and dynamical changes of the Julia set when the parameter C (which can be real or complex) varies in the specific family z^n + C/z^d. (AU)