Dynamics and geometry in dimensions 1, 2 and 3

• Grant number: 16/04687-9
• Support Opportunities: Scholarships abroad - Research
• Start date: August 01, 2016
• End date: January 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: André Salles de Carvalho
• Grantee: André Salles de Carvalho
• Host Investigator: Toby Dixon Harold Hall
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: University of Liverpool, England
• Associated research grant: 11/16265-8 - Low dimensional dynamics, AP.TEM

Abstract

The aim of this proposal is to study dynamics in dimensions 1 and 2 and its connections with geometric structures in dimensions 2 and 3. There are two starting points for the proposed research: first, the existence of ``good'' dynamical models for surface diffeomorphisms and families of such diffeomorphisms and, second, the relationship between 1- and 2-dimensional dynamics with interesting geometric structures on surfaces and 3-manifolds.

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)

BOYLAND, PHILIP; DE CARVALHO, ANDRE; HALL, TOBY. Itineraries for inverse limits of tent maps: A backward view. Topology and its Applications, v. 232, p. 1-12, DEC 1 2017. (16/04687-9)

BOYLAND, PHILIP; DE CARVALHO, ANDRE; HALL, TOBY. Natural extensions of unimodal maps: virtual sphere homeomorphisms and prime ends of basin boundaries. GEOMETRY & TOPOLOGY, v. 25, n. 1, p. 111-228, 2021. (16/04687-9, 11/16265-8)