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Ergodic and qualitative theory of dynamical systems

Grant number: 13/24541-0
Support type:Research Projects - Thematic Grants
Duration: July 01, 2014 - June 30, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Claudio Aguinaldo Buzzi
Grantee:Claudio Aguinaldo Buzzi
Home Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
Pesquisadores principais:
Ali Messaoudi ; Paulo Ricardo da Silva
Assoc. researchers:Benito Frazao Pires ; Cláudio Gomes Pessoa ; Eduardo Garibaldi ; Jéfferson Luiz Rocha Bastos ; Luci Any Francisco Roberto ; Marcelo Messias ; Márcio Ricardo Alves Gouveia ; Pedro Toniol Cardin ; Sylvain Philippe Pierre Bonnot ; Tatiana Miguel Rodrigues ; Tiago de Carvalho ; Vanderlei Minori Horita ; Weber Flávio Pereira
Associated grant(s):18/23190-3 - International Nonlinear Dynamics Conference - NODYCON 2019, AR.EXT
17/19360-8 - Topological dynamics of linear operators, AV.EXT
17/22588-0 - Dynamics, operators and ergodicity, AV.BR
+ associated grants 17/03352-6 - Limit cycles in some piecewise differential systems, AV.EXT
16/02031-9 - Regularization of discontinuously foliated manifolds, AV.EXT
16/07038-1 - The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, AR.EXT - associated grants
Associated scholarship(s):18/19726-5 - Dulac's Problem and of the Focus Center on Two-Dimensional Manifolds, BE.PQ
19/01682-4 - Global Dynamics of Differential Equations, BP.PD
19/06335-0 - Ordinary differential equations and modeling in Biology, BP.IC
+ associated scholarships 19/08303-9 - Qualitative theory and applications of ordinary differential equations with MAPLE software, BP.IC
19/00028-9 - An introduction to the Qualitative Theory of Ordinary Differential Equations, BP.IC
19/00581-0 - Introduction to discrete dynamic systems, BP.IC
18/23194-9 - Global study of reversible vector fields of type (2,0), BP.MS
17/25955-4 - Rigidity of dissipative Lorenz maps with criticality, BE.PQ
17/25021-1 - Local and global aspects of the qualitative theory of ordinary differential equations, BP.IC
17/18255-6 - Closing lemmas and shifts for piecewise smooth vector fields, BP.DD
17/21161-3 - On the number of limit cycles bifurcating from a linear center, BP.IC
17/17877-3 - Introduction to dynamic systems with applications to the modeling of cancer, BP.IC
17/08779-8 - Thom-Smale Program for piecewise smooth differential systems in low dimensions manifolds, BP.DR
17/12581-9 - Theoretical and computational study of ordinary differential equations with software MAPLE, BP.IC
17/07667-1 - An introduction to dynamic systems with applications on Biology, BP.IC
16/22310-0 - Discontinuous foliations and impasses, BP.DR
17/05260-1 - Some distinct formulations of closing Lemmas, BP.MS
15/26161-6 - Julia sets, Vershik adic map and dynamic of operators, BP.PD
16/00242-2 - Bifurcation of piecewise smooth systems with singular borders via regularization, BP.DR
15/26656-5 - Qualitative Theory of Ordinary Differential Equations and computational simulations with MAPLE, BP.IC
15/24803-0 - Limit cycles in planar Filippov system, BP.MS
15/21705-8 - Introduction to smooth and piecewise smooth qualitative theory of differential equations with applications to Mechanics and Electrical Engineering, BP.IC
14/18707-6 - Generic bifurcations and equivalence relations in piecewise smooth vector fields, BP.MS
15/00714-9 - Discontinuous piecewise linear systems, BP.IC
14/21815-5 - Dynamical and ergodic properties of symplectic diffeomorphisms, BE.PQ
14/14096-2 - Global dynamics and integrability of quadratic polynomial differential systems in R3 with symetry, BP.MS - associated scholarships

Abstract

Dynamical systems are one of the best tools for understanding of the mathematical models of experimental sciences. The main goal of this project is to improve the knowledge of these systems obtaining new results with emphasis on the study of the following ten main topics: systems of differential equations piecewise smooth, discontinuous perturbations of centers, systems of quadratic polynomial differential equations in three dimensional space, reversible vector fields, stochastic adding machine and Julia sets, holomorphic dynamics and complex Hénon maps, periodic points for piecewise smooth maps and interval exchange, entropy of symplectic diffeomorphisms, accessibility for partially hyperbolic diffeomorphisms, and selection of measures the Gibbs-absolute zero temperature equilibrium. The main institution is the UNESP - S. J. Rio Preto. The team consists of researchers with experience in advising doctorates and coordinating projects, as well as young researchers. The team has also members from other campuses of UNESP: Bauru, Ilha Solteira, Presidente Prudente, and other institutions of the state of São Paulo: IME-USP, IMECC-UNICAMP and USP-Ribeirão Preto. The project will be guided by the following actions: i) cooperation with high level researches from Brazil and other countries as France, Spain, England, USA, Austria, Chile and Uruguay; ii) participation in conferences and visits to centers of excellence; iii) publication of results in journals of recognized scientific merit. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (38)
(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)
BUZZI, CLAUDIO A.; CARVALHO, TIAGO; EUZEBIO, RODRIGO D.. ON POINCARE BENDIXSON THEOREM AND NON-TRIVIAL MINIMAL SETS IN PLANAR NONSMOOTH VECTOR FIELDS. PUBLICACIONS MATEMATIQUES, v. 62, n. 1, p. 113-131, . (13/24541-0, 14/18508-3, 13/25828-1, 14/02134-7)
GOUVEIA, MARCIO R. A.; LLIBRE, JAUME. PERIODS OF PERIODIC HOMEOMORPHISMS OF PINCHED SURFACES WITH ONE OR TWO BRANCHING POINTS. HOUSTON JOURNAL OF MATHEMATICS, v. 45, n. 4, p. 1227-1243, . (13/24541-0, 13/13344-0)
LOPES, ARTUR O.; MESSAOUDI, ALI; STADLBAUER, MANUEL; VARGAS, VICTOR. Invariant probabilities for discrete time linear dynamics via thermodynamic formalism. Nonlinearity, v. 34, n. 12, p. 8359-8391, . (13/24541-0)
GOUVEIA, MARCIO R. A.; LLIBRE, JAUME; ROBERTO, LUCI ANY. Phase portraits of the quadratic polynomial Lienard differential systems. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. 151, n. 1, p. 202-216, . (13/24541-0)
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)
JIMENEZ, JEIDY J.; LLIBRE, JAUME; MEDRADO, JOAO C.. Crossing limit cycles for piecewise linear differential centers separated by a reducible cubic curve. Electronic Journal of Qualitative Theory of Differential Equations, n. 19, p. 1-48, . (17/03352-6, 13/24541-0)
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)
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)
JIMENEZ, JOHANA; LLIBRE, JAUME; MEDRADO, JOAO C.. CROSSING LIMIT CYCLES FOR A CLASS OF PIECEWISE LINEAR DIFFERENTIAL CENTERS SEPARATED BY A CONIC. Electronic Journal of Differential Equations, . (17/03352-6, 13/24541-0)
BUZZI, CLAUDIO A.; PAZIM, RUBENS; PEREZ-GONZALEZ, SET. Center boundaries for planar piecewise-smooth differential equations with two zones. Journal of Mathematical Analysis and Applications, v. 445, n. 1, p. 631-649, . (13/24541-0)
MESSAOUDI, ALI; VALLE, GLAUCO. Spectra of generalized stochastic adding machines. FUNDAMENTA MATHEMATICAE, v. 241, n. 1, p. 17-43, . (13/24541-0)
PANAZZOLO, DANIEL; DA SILVA, PAULO R.. Regularization of discontinuous foliations: Blowing up and sliding conditions via Fenichel theory. Journal of Differential Equations, v. 263, n. 12, p. 8362-8390, . (13/24541-0, 16/02031-9)
CARDIN, PEDRO TONIOL; LLIBRE, JAUME. Transcritical and zero-Hopf bifurcations in the Genesio system. NONLINEAR DYNAMICS, v. 88, n. 1, p. 547-553, . (13/24541-0)
MESSIAS, MARCELO; REINOL, ALISSON C.. On the formation of hidden chaotic attractors and nested invariant tori in the Sprott A system. NONLINEAR DYNAMICS, v. 88, n. 2, p. 807-821, . (13/24541-0, 13/26602-7)
GOUVEIA, MARCIO R. A.; MESSIAS, MARCELO; PESSOA, CLAUDIO. Bifurcations at infinity, invariant algebraic surfaces, homoclinic and heteroclinic orbits and centers of a new Lorenz-like chaotic system. NONLINEAR DYNAMICS, v. 84, n. 2, p. 703-713, . (13/24541-0, 12/18413-7)
MESSIAS, MARCELO; REINOL, ALISSON C.. On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nos,-Hoover oscillator. NONLINEAR DYNAMICS, v. 92, n. 3, p. 1287-1297, . (13/24541-0, 13/26602-7)
BUZZI, CLAUDIO A.; LLIBRE, JAUME; PAZIM, RUBENS. On the dynamics of the Euler equations on so(4). DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 35, n. 2, . (13/24541-0)
BERNARDES, JR., NILSON C.; CIRILO, PATRICIA R.; DARJI, UDAYAN B.; MESSAOUDI, ALI; PUJALS, ENRIQUE R.. Expansivity and shadowing in linear dynamics. Journal of Mathematical Analysis and Applications, v. 461, n. 1, p. 796-816, . (13/24541-0, 11/11663-5)
LLIBRE, JAUME; MESSIAS, MARCELO; REINOL, ALISSON C.. Quadratic three-dimensional differential systems having invariant planes with total multiplicity nine. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, v. 67, n. 3, p. 569-580, . (13/26602-7, 16/01258-0, 13/24541-0)
BASTOS, JEFFERSON L. R.; BUZZI, CLAUDIO A.; TORREGROSA, JOAN. ORBITALLY SYMMETRIC SYSTEMS WITH APPLICATIONS TO PLANAR CENTERS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v. 20, n. 10, p. 3301-3329, . (17/03352-6, 19/10269-3, 13/24541-0)
BUZZI, CLAUDIO A.; LLIBRE, JAUME. No periodic orbits for the type A Bianchi's systems. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, v. 22, n. 2, p. 170-179, . (13/24541-0)
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, . (13/24541-0, 11/23199-1, 07/06896-5)
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)
MESSIAS, MARCELO; SILVA, RAFAEL PAULINO. Nonchaotic Behavior in Quadratic Three-Dimensional Differential Systems with a Symmetric Jacobian Matrix. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 28, n. 3, . (13/24541-0)
CARDIN, PEDRO TONIOL; TORREGROSA, JOAN. Limit cycles in planar piecewise linear differential systems with nonregular separation line. PHYSICA D-NONLINEAR PHENOMENA, v. 337, p. 67-82, . (13/24541-0)
MESSAOUDI, ALI; VALLE, GLAUCO. Generalized adding machines and Julia sets. COMPTES RENDUS MATHEMATIQUE, v. 354, n. 11, p. 1096-1100, . (13/24541-0)
DALBELO, THAIS MARIA; MESSIAS, MARCELO; REINOL, ALISSON C.. Polynomial Differential Systems in Having Invariant Weighted Homogeneous Surfaces. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 49, n. 1, p. 137-157, . (13/26602-7, 13/24541-0)
CARDIN, PEDRO T.; DE MORAES, JANNE R.; DA SILVA, PAULO R.. Persistence of periodic orbits with sliding or sewing by singular perturbation. Journal of Mathematical Analysis and Applications, v. 423, n. 2, p. 1166-1182, . (13/24541-0, 13/21947-6, 10/17956-1)
MESSIAS, MARCELO; MACIEL, ANDERSON L.. On the Existence of Limit Cycles and Relaxation Oscillations in a 3D van der Pol-like Memristor Oscillator. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 27, n. 7, . (13/24541-0)
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)
BUZZI, CLAUDIO A.; GASULL, ARMENGOL; TORREGROSA, JOAN. Algebraic Limit Cycles in Piecewise Linear Differential Systems. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 28, n. 3, . (17/03352-6, 13/24541-0)
EUZEBIO, RODRIGO D.; GOUVEIA, MARCIO R. A.. Poincare recurrence theorem for non-smooth vector fields. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 68, n. 2, . (13/24541-0, 13/25828-1)
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)
BASTOS, J.; MESSAOUDI, A.; RODRIGUES, T.; SMANIA, D.. A class of cubic Rauzy fractals. THEORETICAL COMPUTER SCIENCE, v. 588, p. 114-130, . (13/24541-0, 08/02841-4)
MESSIAS, MARCELO; REINOL, ALISSON C.. Integrability and Dynamics of Quadratic Three-Dimensional Differential Systems Having an Invariant Paraboloid. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 26, n. 8, . (13/24541-0, 13/26602-7)
LLIBRE, JAUME; MESSIAS, MARCELO; REINOL, ALISSON C.. Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 32, n. 3, p. 374-390, . (13/26602-7, 16/01258-0, 13/24541-0)
BASTOS, JEFFERSON L. R.; BUZZI, CLAUDIO A.; LLIBRE, JAUME; NOVAES, DOUGLAS D.. Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold. Journal of Differential Equations, v. 267, n. 6, p. 3748-3767, . (16/11471-2, 18/16430-8, 13/24541-0)
BUZZI, CLAUDIO A.; MEDRADO, JOAO C.; TORREGROSA, JOAN. Limit cycles in 4-star-symmetric planar piecewise linear systems. Journal of Differential Equations, v. 268, n. 5, p. 2414-2434, . (17/03352-6, 13/24541-0)

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