Control systems, dynamical systems, stochastic dynamical systems, Lie theory and differential geometry

• Grant number: 02/10246-2
• Support Opportunities: Research Projects - Thematic Grants
• Start date: May 01, 2003
• End date: July 31, 2007
• 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
• City of the host institution: Campinas
• Principal investigators: Marco Antônio Teixeira
• Associated research grant(s): 06/53521-4 - Relations between einstein, kahler-einstein and (1,2)-symplectic metrics whit stability on flags., AR.EXT

Abstract

This proposal intends to join different research groups in the Mathematics Institute (IMECC, University of Campinas, UNICAMP) which are interested in geometric properties of dynamical phenomena. These research groups include Control Systems, Dynamical Systems, Stochastic Dynamical Systems, Lie Theory and Differential Geometry. Frequently these fields interact among themselves by the use of similar methods and interdependent results. This proposal includes around 10 research projects, involving 8 researchers from the Mathematics Department of this institute and other Sao Paulo State universities, more than 15 graduate students, as well as many Brazilian and foreigner researchers. This project is planned for a 4 year period and includes the sponsoring of an International Congress on Geometric Nonlinear Control which will be followed by a School on Control Theory, partially supported by CIMPA/France in Julyj2003 (see http:/ /www.ime.unicamp.br/~cntrlO3). (AU)

Scientific publications

(14)

(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)

CORNEA, O.; DE REZENDE, K. A.; DA SILVEIRA, M. R.. Spectral sequences in Conley's theory. Ergodic Theory and Dynamical Systems, v. 30, n. 4, p. 1009-1054, AUG 2010. (02/10246-2)

LAMB, JEROEN S. W.; TEIXEIRA, MARCO ANTONIO; WEBSTER, KEVIN N.. Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in R. Journal of Differential Equations, v. 219, n. 1, p. 78-115, Dec. 2005. (02/10246-2)

BERTOLIM, MARIA ALICE; MELLO, MARGARIDA PINHEIRO; REZENDE, KETTY ABAROA DE. Poincare-Hopf and Morse inequalities for Lyapunov graphs. Ergodic Theory and Dynamical Systems, v. 25, n. 1, p. 1-39, Feb. 2005. (01/04597-4, 02/10246-2, 00/05385-8)

CATUOGNO, PEDRO J.; LEDESMA, DIEGO SEBASTIAN; RUFFINO, PAULO R. C.. Relative rotation number for stochastic systems: dynamical and topological applications. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 23, n. 4, p. 425-435, 2008. (02/10246-2)

PATRAO‚ M.. Morse decomposition of semiflows on topological spaces. Journal of Dynamics and Differential Equations, v. 19, n. 1, p. 181-198, 2007. (02/10246-2)

PATRAO‚ M.; MARTIN‚ L.A.B.S.. Semiflows on topological spaces: chain transitivity and semigroups. Journal of Dynamics and Differential Equations, v. 19, n. 1, p. 155-180, 2007. (02/10246-2)

CATUOGNO, PEDRO; MARTINEZ, FEDERICO; MOLINA, SANDRA. LAGUERRE EXPANSIONS AND PRODUCTS OF DISTRIBUTIONS. COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, v. 23, n. 2, p. 9-pg., 2008-01-01. (02/10246-2)

SAN MARTIN, LUIZ A. B.; SECO, LUCAS. Morse and Lyapunov spectra and dynamics on flag bundles. Ergodic Theory and Dynamical Systems, v. 30, p. 30-pg., 2010-06-01. (02/10246-2)

CORNEA, O.; DE REZENDE, K. A.; DA SILVEIRA, M. R.. Spectral sequences in Conley's theory. Ergodic Theory and Dynamical Systems, v. 30, p. 46-pg., 2010-08-01. (02/10246-2)

SAN MARTIN, LUIZ A. B.; SECO, LUCAS. Morse and Lyapunov spectra and dynamics on flag bundles. Ergodic Theory and Dynamical Systems, v. 30, n. 3, p. 893-922, JUN 2010. (02/10246-2)

JORGE‚ N.L.; RUFFINO‚ P.R.C.; SAN MARTIN‚ L.A.B.. POISSON SPACES FOR PROPER SEMIGROUPS OF SEMI-SIMPLE LIE GROUPS. Stochastics and Dynamics, v. 7, n. 03, p. 273-297, 2007. (02/10246-2)

ROCIO, OSVALDO G. DO; SAN MARTIN, LUIZ A. B.. Connected components of open semigroups in semi-simple Lie groups. Semigroup Forum, v. 69, n. 1, p. 1-29, June 2004. (02/10246-2)

CATUOGNO, PEDRO JOSÉ; RUFFINO, PAULO R. C.. Geometry of stochastic delay differential equations. Electronic Communications in Probability, v. 10, p. 190-195, Sept. 2005. (02/10246-2)

CASAGRANDE, R.; DE REZENDE, K. A.; TEIXEIRA, M. A.. The Conley index for discontinuous vector fields. Geometriae Dedicata, v. 136, n. 1, p. 47-56, OCT 2008. (02/10246-2, 04/10229-6)