Limit Tori in Three-Dimensional Vector Fields

• Grant number: 24/06926-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2024
• Status: Discontinued
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Douglas Duarte Novaes
• Grantee: Lucas Queiroz Arakaki
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 24/15612-6 - Ergodic and qualitative theories of dynamical systems III, AP.TEM
• Associated scholarship(s): 25/08206-4 - Polycycles in planar vector fields: cyclicity and related problems, BE.EP.PD

Abstract

In this project, we tackle two problems concerning invariant tori for three-dimensional vector fields. The first one investigates the existence of invariant tori for vector fields having a 0-nilpotent singular point, i.e. vector fields whose linear term is yx. We propose the study of the invariant tori bifurcation for these vector fields using the Averaging theory to identify a Neimark-Sacker bifurcation at the associated return map, and importing some techniques from the study of nilpotent singular points to classify the tori in their regularity and stability. The second one consists in dealing with a broader problem: the asymptotic growth of the number N(m) of invariant tori with respect to the degree m of a polynomial three-dimensional differential system.

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.)

ARAKAKI, LUCAS QUEIROZ; MELLO, LUIS FERNANDO; RIBEIRO, RONISIO MOISES. Global Stability of the Lengyel-Epstein Systems. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. N/A, p. 6-pg., 2025-09-11. (24/06926-7)

GUSSON, VITOR; PESSOA, CLAUDIO; QUEIROZ, LUCAS. Isochronous centers on center manifolds in R³. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 266, p. 11-pg., 2026-05-01. (24/16727-1, 24/06926-7)