Dynamics of holomorphic correspondences

• Grant number: 10/17397-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2011
• End date: April 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Daniel Smania Brandão
• Grantee: Carlos Alberto Siqueira Lima
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 08/02841-4 - Topology, geometry and ergodic theory of dynamical systems, AP.TEM

Abstract

We will study the dynamics in the complex plane of holomorphic correspondences that appears in a natural way as "analytic extensions'' of the dynamics of the maps |x|^{p/q}+c on the real line.In particular we are interested in the geometric, ergodic and topological properties of the Julia sets of these correspondences when c is small enough.

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)

SIQUEIRA, CARLOS; SMANIA, DANIEL. Holomorphic motions for unicritical correspondences. Nonlinearity, v. 30, n. 8, p. 3104-3125, AUG 2017. (10/17397-2)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

LIMA, Carlos Alberto Siqueira. Dynamics of holomorphic correspondences. 2015. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.