Averaging theory for studying invariant tori and periodic behavior in differential equations and inclusions

• Grant number: 22/09633-5
• Support Opportunities: Regular Research Grants
• Start date: October 01, 2022
• End date: September 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Douglas Duarte Novaes
• Grantee: Douglas Duarte Novaes
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this research project, it will be addressed global aspects of differential equations and inclusions and it is divided into 2 main themes: 1. Bifurcation of Invariant Tori of Differential Equations and 2. Bifurcation of Periodic Solutions of Differential Systems with Low Regularity. In both themes, the main goal consists in developing methods for detecting periodic and quasi-periodic behavior in differential equations and inclusions. (AU)

Scientific publications

(7)

(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)

NOVAES, DOUGLAS D.; PEREIRA, PEDRO C. C. R.. Invariant tori via higher order averaging method: existence, regularity, convergence, stability, and dynamics. MATHEMATISCHE ANNALEN, v. N/A, p. 48-pg., 2023-06-24. (19/10269-3, 18/13481-0, 20/14232-4, 22/09633-5)

CARMONA, VICTORIANO; FERNANDEZ-SANCHEZ, FERNANDO; GARCIA-MEDINA, ELISABETH; NOVAES, DOUGLAS D.. Properties of Poincare half-maps for planar linear systems and some direct applications to periodic orbits of piecewise systems. Electronic Journal of Qualitative Theory of Differential Equations, v. N/A, n. 22, p. 18-pg., 2023-01-01. (19/10269-3, 21/10606-0, 18/13481-0, 22/09633-5)

PEREIRA, PEDRO C. C. R.; NOVAES, DOUGLAS D.; CANDIDO, MURILO R.. A mechanism for detecting normally hyperbolic invariant tori in differential equations. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 177, p. 45-pg., 2023-09-01. (19/05657-4, 22/09633-5, 18/07344-0, 19/10269-3, 21/10606-0, 20/14232-4, 18/13481-0)

CARMONA, VICTORIANO; FERNANDEZ-SANCHEZ, FERNANDO; NOVAES, DOUGLAS D.. Uniform upper bound for the number of limit cycles of planar piecewise linear differential systems with two zones separated by a straight line. Applied Mathematics Letters, v. 137, p. 8-pg., 2023-03-01. (19/10269-3, 21/10606-0, 18/13481-0, 22/09633-5)

CARMONA, VICTORIANO; FERNANDEZ-SANCHEZ, FERNANDO; NOVAES, DOUGLAS D.. A Succinct Characterization of Period Annuli in Planar Piecewise Linear Differential Systems with a Straight Line of Nonsmoothness. JOURNAL OF NONLINEAR SCIENCE, v. 33, n. 5, p. 13-pg., 2023-10-01. (19/10269-3, 21/10606-0, 18/13481-0, 22/09633-5)

CARMONA, VICTORIANO; FERNANDEZ-SANCHEZ, FERNANDO; NOVAES, DOUGLAS D.. Uniqueness and stability of limit cycles in planar piecewise linear differential systems without sliding region. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 123, p. 18-pg., 2023-04-28. (19/10269-3, 21/10606-0, 18/13481-0, 22/09633-5)

ANDRADE, KAMILA S.; GOMIDE, OTAVIO M. L.; NOVAES, DOUGLAS D.. Bifurcation diagrams of global connections in Filippov systems. NONLINEAR ANALYSIS-HYBRID SYSTEMS, v. 50, p. 26-pg., 2023-11-01. (19/10269-3, 18/13481-0, 15/22762-5, 22/09633-5)