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

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

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)