Averaging Theory for studying the periodic solutions of the differential systems and its applications

• Grant number: 13/16492-0
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: January 01, 2014
• End date: December 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marco Antônio Teixeira
• Grantee: Douglas Duarte Novaes
• Supervisor: Jaume Llibre
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Universitat Autònoma de Barcelona (UAB), Spain
• Associated to the scholarship: 12/10231-7 - Regularization and minimal sets for non-smooth dynamical systems, BP.DR

Abstract

Establishing the existence of invariant sets is an important problem for understanding the dynamics of differential systems. Regarding to the periodic orbits there are few theories which allow the study of its existence, non-existence and its stability for smooth differential systems in arbitrary dimensions. One of those is the averaging theory. On the other hand, the mathematical field which study the discontinuous dynamical systems, called Filippov Systems, is a subject that has been developing at a very fast pace in recent years. This field has become certainly one of the common frontiers between Mathematics, Physics, Engineering, and other related sciences. The purpose of this project consists in developing the averaging theory and its applications for studying the periodic solutions of nonsmooth differential systems either continuous or discontinuous in arbitrary dimension. The main tools we shall use are Brouwer degree theory and regularization process for discontinuous systems. (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)

LLIBRE, JAUME; NOVAES, DOUGLAS D.; TEIXEIRA, MARCO ANTONIO. On the periodic solutions of perturbed 4D non-resonant systems. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 9, n. 2, SI, p. 229-250, DEC 2015. (13/16492-0, 12/18780-0)

LLIBRE, JAUME; NOVAES, DOUGLAS D.; TEIXEIRA, MARCO A.. Limit Cycles Bifurcating from the Periodic Orbits of a Discontinuous Piecewise Linear Differentiable Center with Two Zones. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 25, n. 11, OCT 2015. (12/18780-0, 13/16492-0)

NOVAES, DOUGLAS D.; PONCE, ENRIQUE. A Simple Solution to the Braga-Mello Conjecture. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 25, n. 1, JAN 2015. (13/16492-0)

LLIBRE, JAUME; NOVAES, DOUGLAS D.. Improving the averaging theory for computing periodic solutions of the differential equations. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 66, n. 4, p. 1401-1412, AUG 2015. (13/16492-0)

LLIBRE, JAUME; NOVAES, DOUGLAS D.; TEIXEIRA, MARCO A.. On the birth of limit cycles for non-smooth dynamical systems. BULLETIN DES SCIENCES MATHEMATIQUES, v. 139, n. 3, p. 229-244, MAY 2015. (12/18780-0, 13/16492-0)

LLIBRE, JAUME; NOVAES, DOUGLAS D.; TEIXEIRA, MARCO A.. Higher order averaging theory for finding periodic solutions via Brouwer degree. Nonlinearity, v. 27, n. 3, p. 563-583, MAR 2014. (12/18780-0, 13/16492-0)

LLIBRE, JAUME; NOVAES, DOUGLAS D.; TEIXEIRA, MARCO ANTONIO. On the periodic solutions of perturbed 4D non-resonant systems. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 9, n. 2, p. 22-pg., 2015-12-01. (12/18780-0, 13/16492-0)