Thom-Smale Program for piecewise smooth differential systems in low dimensions manifolds

• Grant number: 17/08779-8
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: September 01, 2017
• End date: January 26, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Ana Livia Rodero
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 13/24541-0 - Ergodic and qualitative theory of dynamical systems, AP.TEM
• Associated scholarship(s): 19/00440-7 - Study of limit cycles in piecewise smooth systems on the sphere, BE.EP.DR

Abstract

The project is dedicated to the study of piecewise smooth vector fields, defined in two or three dimensional manifolds. Within this context, a study will first be carried out aiming at a classification of structurally stable systems in two-dimensional compact manifolds. In a second phase we will consider the bifurcation set, which is obtained by excluding the structurally stable systems, and we will make a classification of the systems of codimension one. Finally the project will be concluded with a characterization of structurally stable systems defined in 3-dimensional manifolds that are foliated by compact 2-dimensional 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.)

BUZZI, CLAUDIO A.; RODERO, ANA LIVIA; TORREGROSA, JOAN. Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres. JOURNAL OF NONLINEAR SCIENCE, v. 31, n. 6, DEC 2021. (17/08779-8, 19/10269-3, 19/00440-7)

BUZZI, CLAUDIO A.; RODERO, ANA LIVIA; TEIXEIRA, MARCO A.. Stability conditions for refractive partially integrable piecewise smooth vector fields. PHYSICA D-NONLINEAR PHENOMENA, v. 440, p. 15-pg., 2022-08-08. (18/13481-0, 19/10269-3, 19/00440-7, 17/08779-8)

BUZZI, CLAUDIO A.; RODERO, ANA LIVIA; TORREGROSA, JOAN. 3-dimensional piecewise linear and quadratic vector fields with invariant spheres. Electronic Journal of Qualitative Theory of Differential Equations, v. N/A, n. 43, p. 27-pg., 2024-01-01. (19/00440-7, 17/08779-8, 21/12630-5, 19/10269-3)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

RODERO, Ana Livia. Structural stability, centers and limit cycles for smooth and piecewise-smooth tridimensional vector fields with invariant bidimensional spheres. 2022. Doctoral Thesis - Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto São José do Rio Preto.