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Study of minimal sets in nonsmooth dynamical systems

Grant number: 15/02517-6
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): August 01, 2015
Effective date (End): May 31, 2016
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Cooperation agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
Principal researcher:Marco Antônio Teixeira
Grantee:Douglas Duarte Novaes
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:12/18780-0 - Geometry of control systems, dynamical and stochastics systems, AP.TEM
Associated scholarship(s):15/24841-0 - Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov-Schmidt reduction, BE.EP.PD


Our goal consist in developing and adapting tools to study minimal sets in nonsmooth dynamical systems. As a first direction of study we will look for results on the existence of such sets. Secondly, we will also study the exponentially small splitting of these sets. (AU)

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Scientific publications (6)
(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.; PONCE, GABRIEL; VARAO, REGIS. Chaos Induced by Sliding Phenomena in Filippov Systems. Journal of Dynamics and Differential Equations, v. 29, n. 4, p. 1569-1583, DEC 2017. Web of Science Citations: 1.
LLIBRE, JAUME; NOVAES, DOUGLAS D.; RODRIGUES, CAMILA A. B. Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones. PHYSICA D-NONLINEAR PHENOMENA, v. 353, p. 1-10, SEP 1 2017. Web of Science Citations: 5.
NOVAES, DOUGLAS D.; TORREGROSA, JOAN. On extended Chebyshev systems with positive accuracy. Journal of Mathematical Analysis and Applications, v. 448, n. 1, p. 171-186, APR 1 2017. Web of Science Citations: 10.
ITIKAWA, JACKSON; LLIBRE, JAUME; NOVAES, DOUGLAS D. A new result on averaging theory for a class of discontinuous planar differential systems with applications. REVISTA MATEMATICA IBEROAMERICANA, v. 33, n. 4, p. 1247-1265, 2017. Web of Science Citations: 4.
GOUVEIA, MARCIO R. A.; LLIBRE, JAUME; NOVAES, DOUGLAS D.; PESSOA, CLAUDIO. Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms. Journal of Differential Equations, v. 260, n. 7, p. 6108-6129, APR 5 2016. Web of Science Citations: 1.
LLIBRE, JAUME; NOVAES, DOUGLAS D.; TEIXEIRA, MARCO A. Periodic solutions of Lienard differential equations via averaging theory of order two. Anais da Academia Brasileira de Ciências, v. 87, n. 4, p. 1905-1913, DEC 2015. Web of Science Citations: 0.

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