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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
Principal Investigator: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
Co-Principal Investigators: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
16/09269-0 - The Center-Focus problem, Abelian integrals and the Hilbert's 16th problem, BP.IC
16/06716-6 - Introduction to nilpotent Lie Groups and Lie Algebras, 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)

Scientific publications (57)
(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)
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, OCT 2019. Web of Science Citations: 0.
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, JUL 2019. Web of Science Citations: 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, APR 2019. Web of Science Citations: 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, FEB 5 2019. Web of Science Citations: 0.
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, 2019. Web of Science Citations: 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, DEC 2018. Web of Science Citations: 0.
DEL BARCO, VIVIANA; GRAMA, LINO. On generalized G(2)-structures and T-duality. JOURNAL OF GEOMETRY AND PHYSICS, v. 132, p. 109-113, OCT 2018. Web of Science Citations: 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, SEP 2018. Web of Science Citations: 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, SEP 2018. Web of Science Citations: 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, AUG 15 2018. Web of Science Citations: 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, JUN 2018. Web of Science Citations: 0.
DEL BARCO, VIVIANA; GRAMA, LINO; SORIANI, LEONARDO. T-duality on nilmanifolds. Journal of High Energy Physics, n. 5 MAY 24 2018. Web of Science Citations: 1.
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, MAY 15 2018. Web of Science Citations: 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, MAY 2018. Web of Science Citations: 1.
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, MAR 2018. Web of Science Citations: 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, MAR 2018. Web of Science Citations: 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, JAN 2018. Web of Science Citations: 0.
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, JAN 2018. Web of Science Citations: 3.
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, NOV 2017. Web of Science Citations: 1.
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, JUN 2017. Web of Science Citations: 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, MAY 2017. Web of Science Citations: 1.
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, MAY 2017. Web of Science Citations: 1.
LLIBRE, JAUME; TEIXEIRA, MARCO ANTONIO. Piecewise linear differential systems without equilibria produce limit cycles?. NONLINEAR DYNAMICS, v. 88, n. 1, p. 157-164, APR 2017. Web of Science Citations: 5.
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, MAR 2017. Web of Science Citations: 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, FEB 2017. Web of Science Citations: 2.
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, 2017. Web of Science Citations: 5.
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, NOV 2016. Web of Science Citations: 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, OCT 5 2016. Web of Science Citations: 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, OCT 2016. Web of Science Citations: 0.
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, SEP 2016. Web of Science Citations: 2.
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, SEP 2016. Web of Science Citations: 1.
GASPARIM, ELIZABETH; GRAMA, LINO; MARTIN, LUIZ A. B. SAN. Symplectic Lefschetz fibrations on adjoint orbits. FORUM MATHEMATICUM, v. 28, n. 5, p. 967-979, SEP 2016. Web of Science Citations: 5.
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, SEP 2016. Web of Science Citations: 2.
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, JUN 2016. Web of Science Citations: 1.
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, JUN 2016. Web of Science Citations: 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 APR 2016. Web of Science Citations: 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, JAN 2016. Web of Science Citations: 2.
RUFFINO, PAULO R.; MORGADO, LEANDRO. Geometry of stochastic delay differential equations with jumps in manifolds. Electronic Communications in Probability, v. 21, 2016. Web of Science Citations: 0.
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, DEC 2015. Web of Science Citations: 0.
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.
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, NOV 2015. Web of Science Citations: 18.
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 OCT 2015. Web of Science Citations: 10.
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, OCT 2015. Web of Science Citations: 9.
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 SEP 2015. Web of Science Citations: 0.
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, AUG 2015. Web of Science Citations: 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, JUN 5 2015. Web of Science Citations: 28.
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, MAY 17 2015. Web of Science Citations: 1.
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, MAY 2015. Web of Science Citations: 31.
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, MAY 2015. Web of Science Citations: 1.
RUFFINO, PAULO R. Application of an averaging principle on foliated diffusions: topology of the leaves. Electronic Communications in Probability, v. 20, MAR 20 2015. Web of Science Citations: 0.
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, JAN 2015. Web of Science Citations: 3.
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, DEC 2014. Web of Science Citations: 1.
MARTINS, RICARDO MIRANDA; MEREU, ANA CRISTINA. Limit cycles in discontinuous classical Lienard equations. Nonlinear Analysis: Real World Applications, v. 20, p. 67-73, DEC 2014. Web of Science Citations: 17.
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, OCT 1 2014. Web of Science Citations: 5.
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, MAR 2014. Web of Science Citations: 38.
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, 2014. Web of Science Citations: 2.
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, 2014. Web of Science Citations: 3.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.