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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, 2025
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 grant(s):24/13683-3 - Sub-Riemannian geometry on homogeneous spaces: A control theoretical approach., AV.EXT
23/11422-5 - Geometry of Lie groups: Killing forms and Kähler-like metrics, AV.EXT
Associated scholarship(s):24/06926-7 - Limit Tori in Three-Dimensional Vector Fields, BP.PD
23/04083-0 - Geometry of Control, Dynamical and Stochastic Systems (Geometry / Topology of Homogenous Spaces), BP.PD
23/04851-7 - Bifurcation of invariant manifolds in smooth and non-smooth differential systems, BP.PD
 + associated scholarships 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
23/03430-8 - 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
22/07595-9 - Ad-invariant metrics on Lie algebras, BP.IC
22/07208-5 - An introduction to ergodic theory with applications to number theory, 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

Abstract

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 (48)
(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)
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)
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)
LIMA, D. V. S.; RAMINELLI, S. A.; DE REZENDE, K. A.. HOMOTOPICAL CANCELLATION THEORY FOR GUTIERREZ-SOTOMAYOR SINGULAR FLOWS. JOURNAL OF SINGULARITIES, v. 23, p. 33-91, . (14/11943-6, 18/13481-0, 15/10930-0, 16/24707-4)
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)
CORREA, EDER M.; GRAMA, LINO. Lax formalism for Gelfand-Tsetlin integrable systems. BULLETIN DES SCIENCES MATHEMATIQUES, v. 170, . (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)
GRAMA, LINO; SECO, LUCAS. Second Homotopy Group and Invariant Geometry of Flag Manifolds. Results in Mathematics, v. 75, n. 3, . (18/13481-0)
ANDRADE, KAMILA DA S.; JEFFREY, MIKE R.; MARTINS, RICARDO M.; TEIXEIRA, MARCO A.. Homoclinic Boundary-Saddle Bifurcations in Planar Nonsmooth Vector Fields. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 32, n. 04, p. 27-pg., . (18/13481-0, 21/08031-9, 15/06903-8, 12/18780-0, 18/03338-6, 14/21259-5, 13/07523-9)
AYALA, VICTOR; DA SILVA, ADRIANO; TORREBLANCA, MARIA. Linear control systems on the homogeneous spaces of the 2D Lie group. Journal of Differential Equations, v. 314, p. 21-pg., . (20/12971-4, 18/13481-0)
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)
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., . (19/10269-3, 21/10606-0, 18/13481-0, 22/09633-5)
GRAMA, LINO; MARTINS, RICARDO M.; PATRAO, MAURO; SECO, LUCAS; SPERANCA, LLOHANN. The projected homogeneous Ricci flow and its collapses with an application to flag manifolds. MONATSHEFTE FUR MATHEMATIK, v. 199, n. 3, p. 28-pg., . (18/03338-6, 21/08031-9, 18/13481-0)
CANTARINO, MARISA; VARAO, REGIS. Anosov endomorphisms on the two-torus: regularity of foliations and rigidity. Nonlinearity, v. 36, n. 10, p. 24-pg., . (18/13481-0, 17/06463-3)
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., . (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., . (19/10269-3, 18/13481-0, 15/22762-5, 22/09633-5)
GRAMA, LINO; LIMA, KENNERSON N. S.. Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on maximal flag manifolds. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 73, p. 41-pg., . (18/13481-0)
MONTUFAR, H.; DE REZENDE, K. A.. CONLEY THEORY FOR GUTIERREZ-SOTOMAYOR FIELDS. JOURNAL OF SINGULARITIES, v. 22, p. 37-pg., . (18/13481-0)
NOVAES, DOUGLAS D.; SILVA, LEANDRO A.. ON THE NON-EXISTENCE OF ISOCHRONOUS TANGENTIAL CENTERS IN FILIPPOV VECTOR FIELDS. Proceedings of the American Mathematical Society, v. 150, n. 12, p. 10-pg., . (18/13481-0, 19/10269-3, 21/10606-0)
GRAJALES, BRIAN; GRAMA, LINO.

Invariant Einstein metrics on real flag manifolds with two or three isotropy summands

. JOURNAL OF GEOMETRY AND PHYSICS, v. 176, p. 31-pg., . (21/04003-0, 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)
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)
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)
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)
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)
RODRIGUES, BRUNO A.; SAN MARTIN, LUIZ A. B.; SANTANA, ALEXANDRE J.. Controllability and semigroups of invariant control systems on Sl (n, H). Mathematics of Control, Signals, and Systems (MCSS), v. 34, n. 2, p. 12-pg., . (18/13481-0)
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., . (18/13481-0, 19/10269-3, 19/00440-7, 17/08779-8)
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)
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)
GRAMA, LINO; OLIVEIRA, AILTON R.. Scalar Curvatures of Invariant Almost Hermitian Structures on Flag Manifolds with Two and Three Isotropy Summands. JOURNAL OF GEOMETRIC ANALYSIS, v. 33, n. 10, p. 35-pg., . (21/04065-6, 18/13481-0, 21/04003-0)
BUZZI, CLAUDIO A.; EUZEBIO, RODRIGO D.; MEREU, ANA C.. Bifurcation of Piecewise Smooth Manifolds from 3D Center-Type Vector Fields. Qualitative Theory of Dynamical Systems, v. 22, n. 4, p. 15-pg., . (19/10269-3, 18/13481-0)
NOVAES, DOUGLAS D.. On the Hilbert number for piecewise linear vector fields with algebraic discontinuity set. PHYSICA D-NONLINEAR PHENOMENA, v. 441, p. 15-pg., . (19/10269-3, 18/13481-0, 21/10606-0)
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., . (19/10269-3, 21/10606-0, 18/13481-0, 22/09633-5)
NOVAES, DOUGLAS D.; SILVA, FRANCISCO B.. HIGHER ORDER ANALYSIS ON THE EXISTENCE OF PERIODIC SOLUTIONS IN CONTINUOUS DIFFERENTIAL EQUATIONS VIA DEGREE THEORY. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v. 53, n. 2, p. 15-pg., . (19/10269-3, 18/22689-4, 18/16430-8, 18/13481-0)
ANDRADE, KAMILA DA S.; CESPEDES, OSCAR A. R.; CRUZ, DAYANE R.; NOVAES, DOUGLAS D.. Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear switching curve. Journal of Differential Equations, v. 287, p. 36-pg., . (18/16430-8, 19/10269-3, 18/13481-0)
NOVAES, DOUGLAS D.; RONDON, GABRIEL. On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities. PHYSICA D-NONLINEAR PHENOMENA, v. 442, p. 15-pg., . (19/10269-3, 20/06708-9, 18/13481-0)
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)
LIMA, D. V. S.; DA SILVEIRA, M. R.; VIEIRA, E. R.. Covering action on Conley index theory. Ergodic Theory and Dynamical Systems, v. N/A, p. 33-pg., . (16/24707-4, 20/11326-8, 18/13481-0)
DA SILVA, GUILHERME TAVARES; MARTINS, RICARDO MIRANDA. Dynamics and stability of non-smooth dynamical systems with two switches. NONLINEAR DYNAMICS, v. 108, n. 4, p. 28-pg., . (18/03338-6, 21/08031-9, 18/13481-0)
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)
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)
LIMA, D. V. S.; DE REZENDE, K. A.; DA SILVEIRA, M. R.. Cancellations of periodic orbits for non-singular Morse-Smale flows. Ergodic Theory and Dynamical Systems, v. N/A, p. 49-pg., . (18/13481-0, 16/24707-4, 20/11326-8)
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., . (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., . (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., . (19/05657-4, 22/09633-5, 18/07344-0, 19/10269-3, 21/10606-0, 20/14232-4, 18/13481-0)

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