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Geometry of control, dynamical and stochastic systems

Grant number: 18/13481-0
Support Opportunities:Research Projects - Thematic Grants
Duration: October 01, 2019 - September 30, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Marco Antônio Teixeira
Grantee:Marco Antônio Teixeira
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Pesquisadores principais:
( Atuais )
Ketty Abaroa de Rezende ; Luiz Antonio Barrera San Martin
Pesquisadores principais:
( Anteriores )
Marco Antônio Teixeira
Associated researchers:Adriano João da Silva ; Ana Cristina de Oliveira Mereu ; Caio José Colletti Negreiros ; Christian da Silva Rodrigues ; Christian Horacio Olivera ; Diego Sebastian Ledesma ; Douglas Duarte Novaes ; Eduardo Garibaldi ; Gabriel Ponce ; Iris de Oliveira Zeli ; José Régis Azevedo Varão Filho ; Lino Anderson da Silva Grama ; Mariana Rodrigues da Silveira ; Pedro Jose Catuogno ; Ricardo Miranda Martins ; Viviana Jorgelina Del Barco
Associated scholarship(s):23/06922-9 - Asymptotic behavior of the Hibert number in polynomial and piecewise polynomial planar vector fields, BP.MS
23/07412-4 - Introduction to Symplectic Geometry, BP.IC
23/04083-0 - Geometry of Control, Dynamical and Stochastic Systems (Geometry / Topology of Homogenous Spaces), BP.PD
+ associated scholarships 23/04851-7 - Bifurcation of invariant manifolds in smooth and non-smooth differential systems, BP.PD
23/03430-8 - Sufficient conditions for the realization of Lyapunov graphs as Gutierrez-Sotomayor flows, BP.PD
22/07654-5 - Invariant sets and chaotic behavior in piecewise smooth dynamical systems on compact manifolds of low dimension, BP.DR
22/11934-3 - Geometry of Riemannian Lie groups, BP.MS
22/09603-9 - Positive curvatures, exotic manifolds and Riemannian foliations, BP.PD
22/07208-5 - An introduction to ergodic theory with applications to number theory, BP.IC
22/07595-9 - Ad-invariant metrics on Lie algebras, BP.IC
21/13585-3 - Topological methods and the existence/non-existence problem of Einstein metrics on homogeneous spaces, BP.MS
21/10606-0 - On limit cycles in piecewise linear vector fields with algebraic discontinuity variety, BE.PQ
21/07017-2 - Invariant sets for piecewise smooth differential equations defined on two dimensional compact manifolds, BP.IC
21/02913-0 - Ergodic properties and flexibility of Lyapunov exponents for partially hyperbolic flows, BP.DR
20/14232-4 - Bifurcation of invariant tori of differential systems via higher order averaging theory, BP.DR
20/14316-3 - 3-dimensional Lie Groups, BP.IC
18/07344-0 - Invariant Sets in differential Dynamical Systems: Periodic orbits, Invariant Tori and Algebraic surfaces., BP.PD - associated scholarships


This proposal's main objective is to integrate within the MathematicsInstitute at UNICAMP, the different research groups interested in investigatinggeometric and topological aspects of dynamical phenomenas. The areasthat are being proposed to be integrated in this project are Control Systems,Dynamical Systems, Stochastic Dynamical Systems, Lie Theory and DifferentialGeometry. There is frequent interaction among these groups due tosimilar methods and techniques that are applicable to solving problems inthese areas. This proposal includes several research projects, interdependentin nature, involving 12 associated researchers, 36 graduate students from theMathematics Department of this University as well as almost 70 researchcollaborators from several universities national and international. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (22)
(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.; VARAO, REGIS. A note on invariant measures for Filippov systems. BULLETIN DES SCIENCES MATHEMATIQUES, v. 167, . (18/13481-0, 17/06463-3, 16/22475-9)
NOVAES, DOUGLAS D.; SILVA, LEANDRO A.. Lyapunov coefficients for monodromic tangential singularities in Filippov vector fields. Journal of Differential Equations, v. 300, p. 565-596, . (19/10269-3, 18/13481-0, 18/16430-8)
CARMONA, VICTORIANO; FERNANDEZ-SANCHEZ, FERNANDO; NOVAES, DOUGLAS D.. A new simple proof for Lum-Chua's conjecture. NONLINEAR ANALYSIS-HYBRID SYSTEMS, v. 40, . (18/16430-8, 19/10269-3, 18/13481-0)
NOVAES, DOUGLAS D.. Higher order stroboscopic averaged functions: a general relationship with Melnikov functions. Electronic Journal of Qualitative Theory of Differential Equations, n. 77, . (18/16430-8, 18/13481-0, 19/10269-3)
CASTRO, MATHEUS M.; MARTINS, RICARDO M.; NOVAES, DOUGLAS D.. Anote on Vishik's normal form. Journal of Differential Equations, v. 281, p. 442-458, . (18/03338-6, 18/16430-8, 19/10269-3, 19/06873-2, 18/13481-0, 17/23692-6)
CARDIN, PEDRO TONIOL; NOVAES, DOUGLAS DUARTE. Asymptotic behavior of periodic solutions in one-parameter families of Lienard equations. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 190, . (19/00976-4, 18/13481-0, 19/10269-3, 13/24541-0, 18/16430-8)
CARVALHO, TIAGO; NOVAES, DOUGLAS DUARTE; GONCALVES, LUIZ FERNANDO. Sliding Shilnikov connection in Filippov-type predator-prey model. NONLINEAR DYNAMICS, v. 100, n. 3, . (17/00883-0, 19/10450-0, 18/16430-8, 18/13481-0, 19/10269-3)
LEDESMA, DIEGO S.. A local solution to the Navier?Stokes equations on manifolds via stochastic representation ?. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 198, . (15/07278-0, 18/13481-0)
CANDIDO, MURILO R.; NOVAES, DOUGLAS D.. On the torus bifurcation in averaging theory. Journal of Differential Equations, v. 268, n. 8, p. 4555-4576, . (18/07344-0, 19/05657-4, 18/16430-8, 18/13481-0, 19/10269-3)
CARDOSO, JOAO L.; LLIBRE, JAUME; NOVAES, DOUGLAS D.; TONON, DURVAL J.. Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 35, n. 3, . (18/16430-8, 18/13481-0, 19/10269-3)
NOVAES, DOUGLAS D.; RONDON, GABRIEL. Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles. Nonlinearity, v. 34, n. 6, p. 4202-4263, . (18/16430-8, 19/10269-3, 20/06708-9, 18/13481-0)
AYALA, VICTOR; DA SILVA, ADRIANO. Central periodic points of linear systems. Journal of Differential Equations, v. 272, p. 310-329, . (18/10696-6, 18/13481-0)
LEDESMA, DIEGO S.. Stochastic calculus on Frechet spaces. ADVANCES IN OPERATOR THEORY, v. 6, n. 1, . (18/13481-0, 15/07278-0)
CORREA, EDER M.; GRAMA, LINO. Lax formalism for Gelfand-Tsetlin integrable systems. BULLETIN DES SCIENCES MATHEMATIQUES, v. 170, . (18/13481-0)
GRAMA, LINO; SECO, LUCAS. Second Homotopy Group and Invariant Geometry of Flag Manifolds. Results in Mathematics, v. 75, n. 3, . (18/13481-0)
LLIBRE, JAUME; NOVAES, DOUGLAS D.; ZELI, IRIS O.. Limit cycles of piecewise polynomial perturbations of higher dimensional linear differential systems. REVISTA MATEMATICA IBEROAMERICANA, v. 36, n. 1, p. 291-318, . (18/16430-8, 19/10269-3, 18/13481-0, 13/21078-8)
NOVAES, DOUGLAS D.; SEARA, TERE M.; TEIXEIRA, MARCO A.; ZELI, IRIS O.. Study of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov Systems Having a Twofold Cycle. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 19, n. 2, p. 1343-1371, . (18/13481-0, 13/21078-8, 19/10269-3)
LLIBRE, JAUME; NOVAES, DOUGLAS D.; RODRIGUES, CAMILA A. B.. Bifurcations from families of periodic solutions in piecewise differential systems. PHYSICA D-NONLINEAR PHENOMENA, v. 404, . (18/16430-8, 18/13481-0, 19/10269-3)
BRAUN, FRANCISCO; MEREU, ANA C.. Zero-Hopf bifurcation in a 3D jerk system. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 59, . (18/13481-0, 17/00136-0)
GRAMA, LINO; OLIVEIRA, AILTON R.. Scalar Curvatures of Invariant Almost Hermitian Structures on Generalized Flag Manifolds. Symmetry Integrability and Geometry-Methods and Applications, v. 17, p. 1-30, . (21/04003-0, 18/13481-0)
GOMIDE, OTAVIO M. L.; TEIXEIRA, MARCO A.. hains in 3D Filippov systems: A chaotic phenomeno. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 159, p. 168-195, . (19/01682-4, 18/13481-0)

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