Parabolic phenomena in complex dynamics

• Grant number: 13/20480-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2014
• End date: April 12, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: André Salles de Carvalho
• Grantee: Luciana Luna Anna Lomonaco
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 11/16265-8 - Low dimensional dynamics, AP.TEM

Abstract

The project I propose concerns various aspects of the theory of parabolic bifurcation in both one and several complex variables.In particular, in one variable, the project concerns an extension of the theory of parabolic-like maps(with a the generalization of the theory to degree d parabolic-like mappings andthe unification of the polynomial-like and parabolic-like theories), and the study of several applications of such a theory.Moreover, I would like to study the parabolic phenomena in several complex variables, with particular interest in the Hénon family.

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)

LOMONACO, LUNA; PETERSEN, CARSTEN LUNDE; SHEN, WEIXIAO. ON PARABOLIC EXTERNAL MAPS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 37, n. 10, p. 5085-5104, OCT 2017. (13/20480-7)

LOMONACO, LUNA; PETERSEN, CARSTEN LUNDE. On quasi-conformal (in-) compatibility of satellite copies of the Mandelbrot set: I. INVENTIONES MATHEMATICAE, v. 210, n. 2, p. 615-644, NOV 2017. (13/20480-7)