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Geometry of control systems, dynamical and stochastics systems

Grant number: 12/18780-0
Support type:Research Projects - Thematic Grants
Duration: April 01, 2013 - March 31, 2018
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Marco Antônio Teixeira
Grantee:Marco Antônio Teixeira
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Pesquisadores principais:
Ketty Abaroa de Rezende ; Luiz Antonio Barrera San Martin
Assoc. researchers:Ana Cristina de Oliveira Mereu ; Caio José Colletti Negreiros ; Christian Horacio Olivera ; Diego Sebastian Ledesma ; Douglas Duarte Novaes ; Eduardo Garibaldi ; Gabriel Ponce ; José Régis Azevedo Varão Filho ; Lino Anderson da Silva Grama ; Mariana Rodrigues da Silveira ; Maurício Firmino Silva Lima ; Paulo Regis Caron Ruffino ; Pedro Jose Catuogno ; Ricardo Miranda Martins
Associated grant(s):15/10398-7 - Gibbs measures at zero temperature, AV.EXT
14/17487-2 - Semigroups in semi-simple Lie Groups, AV.EXT
Associated scholarship(s):17/23692-6 - Structural stability of piecewise smooth dynamical systems on torus and spheres, BP.MS
17/23192-3 - An essay about Higgs bundle and applications, BP.MS
17/03675-0 - Topics in symplectic geometry and applications to mirror symmetry, BP.DR
+ associated scholarships 17/04689-4 - Limit cycles for piecewise smooth dynamical systems in dimension n>2 and in compact manifolds, BP.MS
16/25459-4 - Persistence of minimal sets in dynamic systems, BP.MS
16/21975-8 - Piecewise linear dynamical systems (in infinitely many zones): structural stability and asymptotic stability, BP.MS
16/06716-6 - Introduction to nilpotent Lie groups and Lie algebras, BP.IC
16/09269-0 - The Center-Focus problem, Abelian integrals and the Hilbert's 16th problem, BP.IC
16/07029-2 - Invariant generalized complex structures on homogeneous spaces, BP.DR
15/23896-5 - Invariant structures on real flag manifolds, BP.PD
15/22762-5 - Structural Stability of Nonsmooth Systems on Tridimensional Manifolds, BP.DR
15/02517-6 - Study of minimal sets in nonsmooth dynamical systems, BP.PD
15/10937-5 - Generalized complex geometry on homogeneous spaces, T-duality and applications to mirror symmetry, BP.DR
15/02731-8 - Rigidity of partially hyperbolic dynamical systems and Anosov systems, BP.PD
14/11943-6 - Spectral sequences for Morse-Bott and Morse-Novikov flows study, BP.PD
14/12334-3 - Introduction to stochastic dynamics, BP.IC
13/25828-1 - Minimal sets and invariant manifolds in piecewise smooth systems, BP.PD
13/19756-8 - Invariance entropy for semigroups actions in homogeneous spaces, BP.PD
13/18168-5 - Non-smooth Dynamical Systems on the plane, BP.MS
13/20665-7 - Fixed point theorem and applications, BP.IC
13/10467-3 - Geometry of Homogenous space of Loop Groups, BP.DR
13/07523-9 - Bifurcations of Degenerated Cycles in Discontinuous Systems, BP.DR
13/14601-6 - Introduction to the qualitative theory of differential equations, BP.IC
13/04532-7 - Introduction to the planar dynamical systems, BP.IC - associated scholarships

Abstract

This proposal's main objective is to integrate within the Mathematics Institute at UNICAMP, the different research groups interested in investigating geometric and topological aspects of dynamical phenomena. The areas that are being proposed to be integrated in this project are comprised of the Control Systems, Dynamical Systems, Stochastic Dynamical Systems, Lie Theory and Differential Geometry groups. There is frequent interaction among these groups due to similar methods and techniques that are applicable to solving problems in these areas. This proposal includes several research projects, interdependent in nature, involving 12 researchers and 29 graduate students from the Mathematics Department of this University as well as several research collaborators from other State and Federal Universities of the State of São Paulo. We have over 35 international research collaborators and approximately the same number from Brazilian universities. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (60)
(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)
CARDIN, PEDRO T.; DA SILVA, PAULO R.; TEIXEIRA, MARCO A.. THREE TIME SCALE SINGULAR PERTURBATION PROBLEMS AND NONSMOOTH DYNAMICAL SYSTEMS. QUARTERLY OF APPLIED MATHEMATICS, v. 72, n. 4, p. 673-687, . (13/21947-6, 12/18780-0)
LIMA, DAHISY V. DE S.; DE REZENDE, KETTY A.. CONNECTION MATRICES FOR MORSE-BOTT FLOWS. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 44, n. 2, p. 471-495, . (12/18780-0, 10/08579-0)
NEVES, WLADIMIR; OLIVERA, CHRISTIAN. Wellposedness for stochastic continuity equations with Ladyzhenskaya-Prodi-Serrin condition. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, v. 22, n. 5, p. 1247-1258, . (12/18739-0, 12/18780-0, 13/15795-9)
MARTINS, RICARDO MIRANDA; MEREU, ANA CRISTINA; OLIVEIRA, REGILENE D. S.. An estimation for the number of limit cycles in a Lienard-like perturbation of a quadratic nonlinear center. NONLINEAR DYNAMICS, v. 79, n. 1, p. 185-194, . (12/06879-1, 12/18780-0)
RUFFINO, PAULO R.. Application of an averaging principle on foliated diffusions: topology of the leaves. Electronic Communications in Probability, v. 20, . (11/50151-0, 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, . (13/16492-0, 12/18780-0)
AYALA, VICTOR; RIBEIRO, JR., RODOLFO; SAN MARTIN, LUIZ A. B.. CONTROLLABILITY ON SL(2, C) WITH RESTRICTED CONTROLS. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, v. 52, n. 4, p. 2548-2567, . (12/18780-0)
DE CARVALHO, TIAGO; TEIXEIRA, MARCO ANTONIO. Basin of attraction of a cusp-fold singularity in 3D piecewise smooth vector fields. Journal of Mathematical Analysis and Applications, v. 418, n. 1, p. 11-30, . (10/18190-2, 12/00481-6, 12/18780-0)
DE REZENDE, KETTY A.; LEDESMA, GUIDO G. E.; MANZOLI-NETO, OZIRIDE; VAGO, GIOIA M.. Lyapunov graphs for circle valued functions. Topology and its Applications, v. 245, p. 62-91, . (12/18780-0)
RODRIGUES, HILDEBRANDO M.; TEIXEIRA, MARCO A.; GAMEIRO, MARCIO. On Exponential Decay and the Markus-Yamabe Conjecture in Infinite Dimensions with Applications to the Cima System. Journal of Dynamics and Differential Equations, v. 30, n. 3, p. 1199-1219, . (13/07460-7, 16/21032-6, 12/18780-0, 16/08704-5, 15/19165-5)
LLIBRE, JAUME; TEIXEIRA, MARCO ANTONIO. Piecewise linear differential systems with only centers can create limit cycles?. NONLINEAR DYNAMICS, v. 91, n. 1, p. 249-255, . (12/18780-0)
BRAUN, FRANCISCO; LLIBRE, JAUME; MEREU, ANA C.. ISOCHRONICITY FOR TRIVIAL QUINTIC AND SEPTIC PLANAR POLYNOMIAL HAMILTONIAN SYSTEMS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 36, n. 10, p. 5245-5255, . (14/26149-3, 12/18780-0)
AYALA, VICTOR; DA SILVA, ADRIANO; SAN MARTIN, LUIZ A. B.. CONTROL SYSTEMS ON FLAG MANIFOLDS AND THEIR CHAIN CONTROL SETS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 37, n. 5, p. 2301-2313, . (16/11135-2, 13/19756-8, 12/18780-0)
LLIBRE, JAUME; MEREU, ANA C.; NOVAES, DOUGLAS D.. Averaging theory for discontinuous piecewise differential systems. Journal of Differential Equations, v. 258, n. 11, p. 4007-4032, . (12/10231-7, 12/18780-0)
GRAMA, LINO; NEGREIROS, CAIO J. C.; OLIVEIRA, AILTON R.. Invariant almost complex geometry on flag manifolds: geometric formality and Chern numbers. Annali di Matematica Pura ed Applicata, v. 196, n. 1, p. 165-200, . (14/17337-0, 12/18780-0)
NOVAES, DOUGLAS D.; TEIXEIRA, MARCO A.; ZELI, IRIS O.. The generic unfolding of a codimension-two connection to a two-fold singularity of planar Filippov systems. Nonlinearity, v. 31, n. 5, p. 2083-2104, . (16/11471-2, 12/23591-1, 12/18780-0, 13/21078-8)
GASPARIM, ELIZABETH; GRAMA, LINO; SAN MARTIN, LUIZ A. B.. ADJOINT ORBITS OF SEMI-SIMPLE LIE GROUPS AND LAGRANGIAN SUBMANIFOLDS. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 60, n. 2, p. 361-385, . (14/17337-0, 12/18780-0)
DE REZENDE, KETTY A.; VILLAPOUCA, MARIANA G.. DISCRETE CONLEY INDEX THEORY FOR ZERO DIMENSIONAL BASIC SETS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 37, n. 3, p. 1359-1387, . (12/18780-0)
BERTOLIM, MARIA A.; LIMA, DAHISY V. S.; MELLO, MARGARIDA P.; DE REZENDE, KETTY A.; DA SILVEIRA, MARIANA R.. Algebraic and dynamical cancellations associated to spectral sequence. EUROPEAN JOURNAL OF MATHEMATICS, v. 3, n. 2, p. 387-428, . (12/18780-0, 14/11943-6)
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, . (13/16492-0, 12/18780-0)
CARDIN, PEDRO TONIOL; TEIXEIRA, MARCO ANTONIO. A geometric singular perturbation theory approach to constrained differential equations. Mathematische Nachrichten, v. 292, n. 4, p. 892-904, . (12/18780-0, 13/24541-0)
DO PRADO, RAFAELA F.; GRAMA, LINO. On the stability of harmonic maps under the homogeneous Ricci flow. COMPLEX MANIFOLDS, v. 5, n. 1, p. 122-132, . (16/22755-1, 12/18780-0)
GOMIDE, OTAVIO M. L.; TEIXEIRA, MARCO A.. On structural stability of 3D Filippov systems: A semi-local approach. MATHEMATISCHE ZEITSCHRIFT, v. 294, n. 1-2, p. 419-449, . (15/22762-5, 12/18780-0, 16/23716-0)
ANDRADE, K. DA S.; JEFFREY, M. R.; MARTINS, R. M.; TEIXEIRA, M. A.. On the Dulac's problem for piecewise analytic vector fields. Journal of Differential Equations, v. 266, n. 4, p. 2259-2273, . (13/07523-9, 18/03338-6, 12/18780-0, 15/06903-8, 14/21259-5)
SAN MARTIN, LUIZ A. B.; SANTOS, LAERCIO J.. Characteristic functions of semigroups in semi-simple Lie groups. FORUM MATHEMATICUM, v. 31, n. 4, p. 815-842, . (12/18780-0)
BUZZI, CLAUDIO A.; ROBERTO, LUCI ANY F.; TEIXEIRA, MARCO A.. Stability conditions for reversible and partially integrable systems. PORTUGALIAE MATHEMATICA, v. 78, n. 1, p. 43-63, . (12/18780-0, 13/24541-0)
MARTINS, RICARDO MIRANDA; MEREU, ANA CRISTINA. Limit cycles in discontinuous classical Lienard equations. Nonlinear Analysis: Real World Applications, v. 20, p. 67-73, . (10/13371-9, 12/06879-1, 12/18780-0)
ALVES, LUCIANA A.; SAN MARTIN, LUIZ A. B.. Conditions for equality between Lyapunov and Morse decompositions. Ergodic Theory and Dynamical Systems, v. 36, n. 4, p. 1007-1036, . (12/18780-0)
LLIBRE, JAUME; NOVAES, DOUGLAS D.; TEIXEIRA, MARCO A.. Maximum number of limit cycles for certain piecewise linear dynamical systems. NONLINEAR DYNAMICS, v. 82, n. 3, p. 1159-1175, . (12/10231-7, 12/18780-0)
CATUOGNO, PEDRO J.; LEDESMA, DIEGO S.; RUFFINO, PAULO R.. FOLIATED STOCHASTIC CALCULUS: HARMONIC MEASURES. Transactions of the American Mathematical Society, v. 368, n. 1, p. 563-579, . (11/50151-0, 12/18780-0)
MELO, ALISON M.; MORGADO, LEANDRO; RUFFINO, PAULO R.. Topology of Foliations and Decomposition of Stochastic Flows of Diffeomorphisms. Journal of Dynamics and Differential Equations, v. 30, n. 1, p. 39-54, . (11/50151-0, 11/14797-2, 12/18780-0)
GASPARIM, ELIZABETH; GRAMA, LINO; MARTIN, LUIZ A. B. SAN. Symplectic Lefschetz fibrations on adjoint orbits. FORUM MATHEMATICUM, v. 28, n. 5, p. 967-979, . (14/17337-0, 12/10179-5, 12/18780-0)
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, . (13/16492-0, 12/18780-0)
PATRAO, MAURO; SAN MARTIN, LUIZ A. B.. The isotropy representation of a real flag manifold: Split real forms. INDAGATIONES MATHEMATICAE-NEW SERIES, v. 26, n. 3, p. 547-579, . (12/18780-0)
CARVALHO, TIAGO; TEIXEIRA, MARCO A.. On piecewise smooth vector fields tangent to nested tori. Journal of Differential Equations, v. 261, n. 7, p. 4008-4029, . (12/18780-0, 14/02134-7)
FRANZOSA, ROBERT; DE REZENDE, KETTY A.; VIEIRA, EWERTON R.. GENERALIZED TOPOLOGICAL TRANSITION MATRIX. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 48, n. 1, p. 183-212, . (12/18780-0, 10/19230-8)
BERTOLIM, M. A.; LIMA, D. V. S.; MELLO, M. P.; DE REZENDE, K. A.; DA SILVEIRA, M. R.. A global two-dimensional version of Smale's cancellation theorem via spectral sequences. Ergodic Theory and Dynamical Systems, v. 36, n. 6, p. 1795-1838, . (10/08579-0, 12/18780-0)
LLIBRE, JAUME; TEIXEIRA, MARCO A.; ZELI, IRIS O.. Birth of limit cycles for a class of continuous and discontinuous differential systems in (d+2)-dimension. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 31, n. 3, p. 237-250, . (12/23591-1, 12/18780-0, 13/21078-8)
DE REZENDE, KETTY A.; LEDESMA, GUIDO G. E.; MANZOLI NETO, OZIRIDE. Smale flows on S-2 x S-1. Ergodic Theory and Dynamical Systems, v. 35, n. 5, p. 1546-1581, . (12/18780-0)
LLIBRE, JAUME; TEIXEIRA, MARCO ANTONIO. Piecewise linear differential systems without equilibria produce limit cycles?. NONLINEAR DYNAMICS, v. 88, n. 1, p. 157-164, . (12/18780-0)
MEREU, ANA C.; OLIVEIRA, REGILENE; RODRIGUES, CAMILA A. B.. Limit cycles for a class of discontinuous piecewise generalized Kukles differential systems. NONLINEAR DYNAMICS, v. 93, n. 4, p. 2201-2212, . (14/00304-2, 12/18780-0)
ITIKAWA, JACKSON; LLIBRE, JAUME; MEREU, ANA CRISTINA; OLIVEIRA, REGILENE. LIMIT CYCLES IN UNIFORM ISOCHRONOUS CENTERS OF DISCONTINUOUS DIFFERENTIAL SYSTEMS WITH FOUR ZONES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 22, n. 9, p. 3259-3272, . (14/00304-2, 12/18780-0, 15/07612-7)
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, . (13/16492-0, 12/18780-0)
CARVALHO, TIAGO; TEIXEIRA, MARCO ANTONIO; TONON, DURVAL JOSE. Asymptotic stability and bifurcations of 3D piecewise smooth vector fields. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 67, n. 2, . (12/18780-0, 14/02134-7, 12/00481-6)
BUZZI, C. A.; EUZEBIO, R. D.; MEREU, A. C.. Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder. BULLETIN DES SCIENCES MATHEMATIQUES, v. 140, n. 5, p. 519-540, . (14/18508-3, 12/18780-0, 13/24541-0, 13/25828-1)
RUFFINO, PAULO R.; MORGADO, LEANDRO. Geometry of stochastic delay differential equations with jumps in manifolds. Electronic Communications in Probability, v. 21, . (11/50151-0, 12/18780-0)
RODRIGUES, CHRISTIAN S.; RUFFINO, PAULO R. C.. A family of rotation numbers for discrete random dynamics on the circle. Stochastics and Dynamics, v. 15, n. 3, . (11/50151-0, 12/18780-0)
MELO, ALISON M.; MORGADO, LEANDRO B.; RUFFINO, PAULO R.. DECOMPOSITION OF STOCHASTIC FLOWS GENERATED BY STRATONOVICH SDES WITH JUMPS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 21, n. 9, SI, p. 3209-3218, . (11/50151-0, 15/07278-0, 11/14797-2, 12/18780-0)
MORGADO, LEANDRO; RUFFINO, PAULO R.. Extension of time for decomposition of stochastic flows in spaces with complementary foliations. Electronic Communications in Probability, v. 20, p. 1-9, . (11/14797-2, 11/50151-0, 12/18780-0)
BUZZI, CLAUDIO A.; SILVA LIMA, MAURICIO FIRMINO; TORREGROSA, JOAN. Limit cycles via higher order perturbations for some piecewise differential systems. PHYSICA D-NONLINEAR PHENOMENA, v. 371, p. 28-47, . (17/03352-6, 12/18780-0, 13/24541-0)
LIMA, DAHISY V. DE S.; MANZOLI NETO, OZIRIDE; DE REZENDE, KETTY A.; DA SILVEIRA, MARIANA R.. CANCELLATIONS FOR CIRCLE-VALUED MORSE FUNCTIONS VIA SPECTRAL SEQUENCES. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 51, n. 1, p. 259-311, . (15/10930-0, 12/18780-0, 14/11943-6)
CARDIN, PEDRO TONIOL; TEIXEIRA, MARCO ANTONIO. Fenichel Theory for Multiple Time Scale Singular Perturbation Problems. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 16, n. 3, p. 1425-1452, . (13/24541-0, 13/21947-6, 12/18780-0)
FREITAS, ANA P. C.; DEL BARCO, VIVIANA; SAN MARTIN, LUIZ A. B.. Invariant almost complex structures on real flag manifolds. Annali di Matematica Pura ed Applicata, v. 197, n. 6, p. 1821-1844, . (17/13725-4, 12/18780-0, 15/23896-5)
DEL BARCO, VIVIANA; GRAMA, LINO; SORIANI, LEONARDO. T-duality on nilmanifolds. Journal of High Energy Physics, n. 5, . (15/10937-5, 12/18780-0, 16/22755-1, 15/23896-5, 17/13725-4)
LUQUE JUSTO, CLAUDIA; LEDESMA, DIEGO SEBASTIAN; SILVA, FABIANO BORGES. An isometric embedding of the g(t)-Brownian motion with application in stability and homotopy group. Stochastics and Dynamics, v. 19, n. 6, . (15/07278-0, 12/18780-0, 18/16568-0)
LLIBRE, JAUME; TEIXEIRA, MARCO ANTONIO. Periodic orbits of continuous and discontinuous piecewise linear differential systems via first integrals. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 12, n. 1, p. 121-135, . (12/18780-0)
LEDESMA, DIEGO SEBASTIAN; BORGES DA SILVA, FABIANO. Decomposition of stochastic flow and an averaging principle for slow perturbations. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 35, n. 4, p. 625-654, . (15/07278-0, 18/16568-0, 12/18780-0)
LIMA, D. V. S.; MANZOLI NETO, O.; DE REZENDE, K. A.. On handle theory for Morse-Bott critical manifolds. Geometriae Dedicata, v. 202, n. 1, p. 265-309, . (12/18780-0, 16/24707-4, 14/11943-6)
DEL BARCO, VIVIANA; BARRERA SAN MARTIN, LUIZ ANTONIO. De Rham 2-Cohomology of Real Flag Manifolds. Symmetry Integrability and Geometry-Methods and Applications, v. 15, . (17/13725-4, 12/18780-0, 15/23896-5)
DEL BARCO, VIVIANA; GRAMA, LINO. On generalized G(2)-structures and T-duality. JOURNAL OF GEOMETRY AND PHYSICS, v. 132, p. 109-113, . (17/13725-4, 16/22755-1, 12/18780-0, 15/23896-5)

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