Geometry of control, dynamical and stochastic systems

• Grant number: 07/06896-5
• Support Opportunities: Research Projects - Thematic Grants
• Start date: July 01, 2008
• End date: June 30, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Luiz Antonio Barrera San Martin
• Grantee: Luiz Antonio Barrera San Martin
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Pesquisadores principais: Ketty Abaroa de Rezende ; Marco Antônio Teixeira
• Associated researchers: Alberto Masayoshi Faria Ohashi ; Ali Messaoudi ; Caio José Colletti Negreiros ; Claudio Aguinaldo Buzzi ; Lucas Conque Seco Ferreira ; Luciana de Fátima Martins ; Maurício Firmino Silva Lima ; Paulo Regis Caron Ruffino ; Paulo Ricardo da Silva ; Pedro Jose Catuogno ; Ronan Antonio dos Reis ; Vanderlei Minori Horita
• Associated research grant(s): 10/17450-0 - Accessibility for partially hyperbolic diffeomorphisms, AV.EXT; 09/18338-2 - Bifurcation in dynamical systems: non-autonomous, discontinuous, control and random context, AV.EXT
• Associated scholarship(s): 12/12025-5 - Dynamics in discontinuous systems and in continuous systems near systems with symmetries, BE.PQ; 12/10231-7 - Regularization and minimal sets for non-smooth dynamical systems, BP.DR; 11/22529-8 - Bifurcations of three-parameter families of non-smooth planar systems, BP.DR; + associated scholarships 11/14797-2 - Stochastic dynamics in foliated spaces, BP.DD; 11/13730-1 - Semigroups in Kac-Moody groups, BP.DR; 11/03140-2 - Invariance entropy of control systems on flag manifolds and homogeneous spaces, BP.PD; 11/03896-0 - Periodic orbits of some coupled differential equations, BP.MS; 11/03486-6 - Closed Circuit Optimization in Oriented Graphs, BP.IC; 10/17956-1 - Minimal Sets of Piecewise Linear Systems, BP.DR; 10/18015-6 - A study for minimal sets in non-smooth systems in dimensions two and three, BP.DR; 10/18624-2 - On Singularly Perturbed Filippov Systems, BP.PD; 10/19230-8 - Transition Matrix Theory, BP.DR; 10/19731-7 - Stochastic Adding Machine and Julia Sets, BP.DR; 10/12755-8 - Cellular decompositions of homogeneous spaces, BP.MS; 10/13371-9 - Synchronization of non-smooth dynamical systems, BP.PD; 10/17034-7 - Differential geometry on homogeneous spaces, BP.PD; 10/18664-4 - Unfolding Heterodimensional Cycles for volume preserving diffeomorphisms, BP.PD; 10/18190-2 - Singularities of 3D piecewise smooth Filippov systems, BP.PD; 10/15130-9 - Qualitative theory of differential equations and compactification of vector fields, BP.IC; 10/08579-0 - Transition Matrices associated with the Morse-Witten Complex, BP.DR; 10/11323-7 - Injectivity of mappings and solvability for partial differentiable operators, BP.PD; 09/12337-4 - The study of the Morse-Witten Complex via Spectral Sequences, BP.MS; 09/08946-5 - Symmetries and Discontinuous Systems, BP.DR; 09/07744-0 - Substitutions, Numeration Systems and Rauzy Fractals, BP.PD; 09/05778-4 - Minimal set in pertubations of reversible and/or Hamiltonian systems, BP.PD; 08/07337-2 - Singularities in Non-Smooth Dynamical Systems, BP.MS; 08/09120-0 - Stochastic calculus on foliations, BP.PD; 07/07843-2 - Study of reversible systems in two-dimensional embedding manifolds in R3, BP.PD; 08/00628-1 - Spectral sequences in Conley index theory., BP.PD; 07/07957-8 - Differential equations with impasses and singular perturbation, BP.DR; 07/08454-0 - Substitutions, Rauzy Fractals and Dynamics, BP.DR; 07/08707-5 - Study of minimal sets for discontinuous systems via singular perturbations, BP.DR - associated scholarships

Abstract

The aim of this project is to integrate research groups from the Mathematics Institute of the University of Campinas with groups from other institutions whose research area are linked either by common mathematical questions, interdependent results or by common, similar or complementary methods. The research areas of groups which share similarity and commom methods in this project include: control systems, dynamical systems, stochastic dynamical systems, Lie theory and differential geometry. In the body of the project we enumerate in details the topics where we shall concentrate the research. The topics proposed here are essentially already in progress, they correspond to the natural continuity of the research which has been done by the members of the project. We adapt some related topics to increase the colaboration among the members. (AU)

Scientific publications

(54)

(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)

LLIBRE, JAUME; TEIXEIRA, MARCO ANTONIO. On the periodic orbits of the fourth-order differential equation u `'''+qu `'-u = epsilon F (u, u `, u `', u `''). Journal of Mathematical Analysis and Applications, v. 387, n. 1, p. 181-188, MAR 1 2012. (07/06896-5)

MEREU, ANA CRISTINA; TEIXEIRA, MARCO ANTONIO. REVERSIBILITY AND BRANCHING OF PERIODIC ORBITS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 33, n. 3, SI, p. 1177-1199, MAR 2013. (07/06896-5)

SECO, LUCAS; SAN MARTIN, LUIZ A. B.. Counting geodesics on compact Lie groups. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 56, p. 325-343, FEB 2018. (07/06896-5)

LLIBRE, JAUME; TEIXEIRA, MARCO ANTONIO. Limit cycles for m-piecewise discontinuous polynomial Li,nard differential equations. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 66, n. 1, p. 51-66, FEB 2015. (07/06896-5)

DOS SANTOS, ARIANE LUZIA; SAN MARTIN, LUIZ A. B.. A method to find generators of a semi-simple Lie group via the topology of its flag manifolds. Semigroup Forum, v. 95, n. 2, p. 259-280, OCT 2017. (07/06896-5)

CATUOGNO, PEDRO J.; DA SILVA, FABIANO B.; RUFFINO, PAULO R.. DECOMPOSITION OF STOCHASTIC FLOWS WITH AUTOMORPHISM OF SUBBUNDLES COMPONENT. Stochastics and Dynamics, v. 12, n. 2, JUN 2012. (07/06896-5)

COLONIUS, FRITZ; SAN MARTIN, LUIZ A. B.; DA SILVA, ADRIANO J.. Topological Fiber Entropy for Linear Flows on Vector Bundles. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, v. 20, n. 4, p. 475-490, OCT 2014. (07/06896-5)

LLIBRE, J.; TEIXEIRA, M. A.; TORREGROSA, J.. LOWER BOUNDS FOR THE MAXIMUM NUMBER OF LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH A STRAIGHT LINE OF SEPARATION. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 23, n. 4, APR 2013. (07/06896-5)

DOS SANTOS, ARIANE L.; SAN MARTIN, LUIZ A. B.. Controllability of control systems on complex simple lie groups and the topology of flag manifolds. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, v. 19, n. 2, p. 157-171, APR 2013. (07/06896-5)

MARTINS, RICARDO MIRANDA; TEIXEIRA, MARCO ANTONIO. ON THE SIMILARITY OF HAMILTONIAN AND REVERSIBLE VECTOR FIELDS IN 4D. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v. 10, n. 4, p. 1257-1266, JUL 2011. (07/06896-5, 07/05215-4)

TEIXEIRA, MARCO A.; MARTINS, RICARDO M.. Reversible-equivariant systems and matricial equations. Anais da Academia Brasileira de Ciências, v. 83, n. 2, p. 375-390, JUN 2011. (07/06896-5, 07/05215-4)

ARTES, JOAN C.; LLIBRE, JAUME; TEIXEIRA, MARCO ANTONIO. A universal constant for semistable limit cycles. COMPUTATIONAL & APPLIED MATHEMATICS, v. 30, n. 2, p. 463-483, 2011. (07/06896-5)

ALVES, LUCIANA A.; SAN MARTIN, LUIZ A. B.. MULTIPLICATIVE ERGODIC THEOREM ON FLAG BUNDLES OF SEMI-SIMPLE LIE GROUPS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 33, n. 4, p. 1247-1273, APR 2013. (07/06896-5)

NEGREIROS, CAIO J. C.; GRAMA, LINO; SAN MARTIN, LUIZ A. B.. Invariant Hermitian structures and variational aspects of a family of holomorphic curves on flag manifolds. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v. 40, n. 1, p. 105-123, JUN 2011. (07/06896-5)

BERTOLIM, M. A.; DE REZENDE, K. A.; MANZOLI NETO, O.; VAGO, G. M.. On the variations of the Betti numbers of regular levels of Morse flows. Topology and its Applications, v. 158, n. 6, p. 761-774, APR 1 2011. (07/06896-5, 09/05934-6)

LLIBRE, JAUME; MEREU, ANA CRISTINA; TEIXEIRA, MARCO A.. INVARIANT TORI FULFILLED BY PERIODIC ORBITS FOR FOUR-DIMENSIONAL C-2 DIFFERENTIAL SYSTEMS IN THE PRESENCE OF RESONANCE. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 20, n. 10, p. 3341-3344, OCT 2010. (09/05778-4, 07/06896-5)

LLIBRE, JAUME; MARTINS, RICARDO MIRANDA; TEIXEIRA, MARCO ANTONIO. Periodic orbits, invariant tori, and cylinders of Hamiltonian systems near integrable ones having a return map equal to the identity. Journal of Mathematical Physics, v. 51, n. 8, AUG 2010. (07/06896-5, 07/05215-4)

SILVA LIMA, MAURICIO FIRMINO; TEIXEIRA, MARCO ANTONIO. Families of periodic orbits in resonant reversible systems. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 40, n. 4, p. 511-537, DEC 2009. (07/06896-5)

LLIBRE, JAUME; MEREU, ANA CRISTINA; TEIXEIRA, MARCO A.. Limit cycles of resonant four-dimensional polynomial systems. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 25, n. 2, p. 145-158, 2010. (07/06896-5)

LLIBRE, JAUME; MARTINS, RICARDO MIRANDA; TEIXEIRA, MARCO ANTONIO. ON THE BIRTH OF MINIMAL SETS FOR PERTURBED REVERSIBLE VECTOR FIELDS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 31, n. 3, p. 763-777, NOV 2011. (07/05215-4, 07/06896-5)

GRAMA, LINO; NEGREIROS, CAIO J. C.. Equigeodesics on Generalized Flag Manifolds with Two Isotropy Summands. Results in Mathematics, v. 60, n. 1-4, p. 405-421, OCT 2011. (07/06896-5)

BUZZI, CLAUDIO; PESSOA, CLAUDIO; TORREGROSA, JOAN. PIECEWISE LINEAR PERTURBATIONS OF A LINEAR CENTER. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 33, n. 9, p. 3915-3936, SEP 2013. (11/13152-8, 07/06896-5)

BUZZI, CLAUDIO A.; LLIBRE, JAUME. On the periodic solutions of the static, spherically symmetric Einstein-Yang-Mills equations. Journal of Mathematical Physics, v. 53, n. 12, DEC 2012. (07/06896-5)

DO ROCIO, OSVALDO G.; SAN MARTIN, LUIZ A. B.; VERDI, MARCOS A.. Sernigroup Actions on Adjoint Orbits. JOURNAL OF LIE THEORY, v. 22, n. 4, p. 931-948, 2012. (07/06896-5)

CASSIANO, JEFERSON; SILVA LIMA, MAURICIO FIRMINO; FONSECA, ANDRE. Normally Hyperbolic Sets in Discontinuous Dry Friction Oscillator. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 25, n. 6, JUN 2015. (07/06896-5)

MARTINS, RICARDO MIRANDA; TEIXEIRA, MARCO ANTONIO. MINIMAL SETS IN DOUBLE-PERTURBED DIFFERENTIAL EQUATIONS. HOUSTON JOURNAL OF MATHEMATICS, v. 41, n. 2, p. 491-512, 2015. (07/05215-4, 07/06896-5)

PIRES, BENITO; TEIXEIRA, MARCO ANTONIO. On global linearization of planar involutions. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 43, n. 4, p. 637-653, DEC 2012. (09/02380-0, 07/06896-5, 08/02841-4)

RABELO, LONARDO; SAN MARTIN, LUIZ A. B.. Cellular homology of real flag manifolds. INDAGATIONES MATHEMATICAE-NEW SERIES, v. 30, n. 5, p. 745-772, SEP 2019. (08/04628-6, 07/06896-5)

BAEZ, JHOAN; SAN MARTIN, LUIZ A. B.. Deformations of adjoint orbits for semisimple Lie algebras and Lagrangian submanifolds. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 75, APR 2021. (07/06896-5)

LLIBRE, JAUME; MEREU, ANA CRISTINA; TEIXEIRA, MARCO ANTONIO. Limit cycles of the generalized polynomial Lienard differential equations. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, v. 148, p. 21-pg., 2010-03-01. (07/06896-5)

LLIBRE, JAUME; TEIXEIRA, MARCO ANTONIO. PERIODIC SOLUTIONS OF DISCONTINUOUS SECOND ORDER DIFFERENTIAL SYSTEMS. JOURNAL OF SINGULARITIES, v. 10, p. 8-pg., 2014-01-01. (07/06896-5)

FRANZOSA, R.; DE REZENDE, K. A.; DA SILVEIRA, M. R.. Continuation and bifurcation associated to the dynamical spectral sequence. Ergodic Theory and Dynamical Systems, v. 34, p. 39-pg., 2014-12-01. (07/06896-5)

MEREU, ANA CRISTINA; TEIXEIRA, MARCO ANTONIO. REVERSIBILITY AND BRANCHING OF PERIODIC ORBITS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 33, n. 3, p. 23-pg., 2013-03-01. (07/06896-5)

LLIBRE, JAUME; MEREU, ANA CRISTINA; TEIXEIRA, MARCO ANTONIO. Limit cycles of the generalized polynomial Lienard differential equations. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, v. 148, n. 2, p. 363-383, MAR 2010. (07/06896-5)

FRANZOSA, R.; DE REZENDE, K. A.; DA SILVEIRA, M. R.. Continuation and bifurcation associated to the dynamical spectral sequence. Ergodic Theory and Dynamical Systems, v. 34, n. 6, p. 1849-1887, DEC 2014. (07/06896-5)

DOS REIS, RONAN A.; SAN MARTIN, LUIZ A. B.. Reversibility properties of semigroup actions on homogeneous spaces. Semigroup Forum, v. 84, n. 3, p. 472-486, JUN 2012. (07/06896-5)

AYALA, V.; RODRIGUEZ, J. C.; SAN MARTIN, L. A. B.. OPTIMALITY ON HOMOGENEOUS SPACES, AND THE ANGLE SYSTEM ASSOCIATED WITH A BILINEAR CONTROL SYSTEM. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, v. 48, n. 4, p. 2636-2650, 2009. (07/06896-5)

PATRAO, MAURO; MARTIN, LUIZ A. B. SAN; SECO, LUCAS. Conley indexes and stable sets for flows on flag bundles. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 24, n. 2, p. 249-276, 2009. (07/06896-5)

COHEN, NIR; GRAMA, LINO; NEGREIROS, CAIO J. C.. EQUIGEODESICS ON FLAG MANIFOLDS. HOUSTON JOURNAL OF MATHEMATICS, v. 37, n. 1, p. 113-125, 2011. (07/06896-5)

BUZZI, CLAUDIO A.; DE CARVALHO, TIAGO; TEIXEIRA, MARCO A.. Birth of limit cycles bifurcating from a nonsmooth center. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 102, n. 1, p. 36-47, JUL 2014. (07/06896-5, 12/00481-6)

JACQUEMARD, A.; TEIXEIRA, M. A.. Periodic solutions of a class of non-autonomous second order differential equations with discontinuous right-hand side. PHYSICA D-NONLINEAR PHENOMENA, v. 241, n. 22, p. 2003-2009, NOV 15 2012. (07/06896-5)

BUZZI, CLAUDIO A.; DE CARVALHO, TIAGO; TEIXEIRA, MARCO A.. On 3-Parameter Families of Piecewise Smooth Vector Fields in the Plane. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 11, n. 4, p. 1402-1424, 2012. (10/18190-2, 07/06896-5, 12/00481-6, 07/08707-5)

CORBERA, MONTSERRAT; LLIBRE, JAUME; ANTONIO TEIXEIRA, MARCO. Symmetric periodic orbits near a heteroclinic loop in R-3 formed by two singular points, a semistable periodic orbit and their invariant manifolds. PHYSICA D-NONLINEAR PHENOMENA, v. 238, n. 6, p. 699-705, APR 1 2009. (07/06896-5)

BUZZI, CLAUDIO AGUINALDO; DE CARVALHO, TIAGO; TEIXEIRA, MARCO ANTONIO. ON THREE-PARAMETER FAMILIES OF FILIPPOV SYSTEMS - THE FOLD-SADDLE SINGULARITY. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 22, n. 12, DEC 2012. (10/18190-2, 07/06896-5, 12/00481-6, 07/08707-5)

EL ABDALAOUI, EL HOUCEIN; BONNOT, SYLVAIN; MESSAOUDI, ALI; SESTER, OLIVIER. ON THE FIBONACCIC OMPLEX DYNAMICAL SYSTEMS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 36, n. 5, p. 2449-2471, MAY 2016. (13/24541-0, 07/06896-5, 11/23199-1)

LLIBRE, J.; TEIXEIRA, M. A.. On the stable limit cycle of a weight-driven pendulum clock. European Journal of Physics, v. 31, n. 5, p. 1249-1254, SEP 2010. (07/06896-5)

CARDIN, PEDRO TONIOL; DA SILVA, PAULO RICARDO; TEIXEIRA, MARCO ANTONIO. Implicit differential equations with impasse singularities and singular perturbation problems. Israel Journal of Mathematics, v. 189, n. 1, p. 307-322, JUN 2012. (07/06896-5, 07/07957-8)

BUZZI, C. A.; LLIBRE, J.; MEDRADO, J. C.. On the limit cycles of a class of piecewise linear differential systems in R-4 with two zones. MATHEMATICS AND COMPUTERS IN SIMULATION, v. 82, n. 4, p. 533-539, DEC 2011. (07/06896-5)

SILVA LIMA, MAURICIO FIRMINO; TEIXEIRA, MARCO ANTONIO. Homoclinic orbits in degenerate reversible-equivariant systems in R-6. Journal of Mathematical Analysis and Applications, v. 403, n. 1, p. 155-166, JUL 1 2013. (07/06896-5)

NEGREIROS, CAIO J. C.; GRAMA, LINO; DA SILVA, NEITON P.. Variational results on flag manifolds: Harmonic maps, geodesics and Einstein metrics. Journal of Fixed Point Theory and Applications, v. 10, n. 2, p. 307-325, DEC 2011. (07/06896-5, 10/17034-7)

MESSAOUDI, ALI; SESTER, OLIVIER; VALLE, GLAUCO. SPECTRUM OF STOCHASTIC ADDING MACHINES AND FIBERED JULIA SETS. Stochastics and Dynamics, v. 13, n. 3, SEP 2013. (07/06896-5, 11/23199-1)

BUZZI, CLAUDIO A.; LLIBRE, JAUME. Hopf bifurcation in the full repressilator equations. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 38, n. 7, p. 1428-1436, MAY 15 2015. (07/06896-5)

LLIBRE, JAUME; TEIXEIRA, MARCO ANTONIO. On the periodic orbits of the fourth-order differential equation u ''''+qu ''-u = epsilon F (u, u ', u '', u '''). Journal of Mathematical Analysis and Applications, v. 387, n. 1, p. 8-pg., 2012-03-01. (07/06896-5)

BRAUN, FRANCISCO; DOS SANTOS FILHO, JOSE RUIDIVAL; TEIXEIRA, MARCO ANTONIO. Foliations, solvability, and global injectivity. ARCHIV DER MATHEMATIK, v. 119, n. 6, p. 17-pg., 2022-10-11. (17/00136-0, 07/08231-0, 10/11323-7, 07/06896-5, 14/26149-3)