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Singularities of differentiable mappings: theory and applications

Grant number: 14/00304-2
Support type:Research Projects - Thematic Grants
Duration: June 01, 2014 - May 31, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Maria Aparecida Soares Ruas
Grantee:Maria Aparecida Soares Ruas
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Co-Principal Investigators:Farid Tari ; Marcelo José Saia
Assoc. researchers:Ana Claudia Nabarro ; Bruna Orefice Okamoto ; Eliris Cristina Rizziolli ; Grazielle Feliciani Barbosa ; João Carlos Ferreira Costa ; João Nivaldo Tomazella ; Luciana de Fátima Martins ; Michelle Ferreira Zanchetta Morgado ; Míriam Garcia Manoel ; Nivaldo de Góes Grulha Júnior ; Raimundo Nonato Araújo dos Santos ; Raúl Adrián Oset Sinha ; Regilene Delazari dos Santos Oliveira ; Roberta Godoi Wik Atique ; Serguei Agafonov ; Victor Hugo Jorge Pérez
Associated grant(s):18/09297-0 - Topology and geometry of real and complex singularities, AV.EXT
18/07040-1 - Topology and invariants of maps between varieties, AV.EXT
17/01410-9 - Global dynamical aspects of Abel equations of the third kind, AV.EXT
+ associated grants 17/06176-4 - Mathematical Congress of the Americas 2017, AR.EXT
16/19436-1 - The Zariski's approach for resolution of singularities, AV.EXT
16/08929-7 - Methods of commutative algebra and algebraic geometry in singularity theory, AV.BR
15/06697-9 - Characteristic classes and intersection homology, AV.EXT - associated grants
Associated scholarship(s):19/00194-6 - Geometry of singular surfaces in $\mathbb{R}^4$, BP.PD
19/02068-8 - Singularities of maps and characteristic classes, BP.DR
18/17712-7 - Geometry of singular surfaces, BP.DR
+ associated scholarships 18/18791-8 - Curves and introduction to singularity theory, BP.IC
18/19525-0 - Introduction to algebraic topology, BP.IC
17/23555-9 - Singularities of Hamiltonian Systems with constraints, BP.PD
18/07176-0 - Invariant algebraic curves and integrability in differentiable polynomial systems, BP.IC
17/26168-6 - An Introduction to algebraic geometry, BP.IC
17/20243-6 - An introduction to dynamical systems and bifurcations applied to the Hodgkin-Huxley neuronal model, BP.IC
17/15369-0 - Polar singularity of a flat curve germ , BP.PD
16/23906-3 - Vanishing homology and multiple-point spaces of singular maps, BP.PD
17/08540-5 - The Poincaré-Hopf Theorem, BP.IC
16/14580-7 - Applications of singularity theory: differential geometry and algebraic geometry, BP.PD
16/21226-5 - Differential geometry of the focal set, BP.MS
16/14330-0 - Lipschitz geometry of stratified spaces, BP.PD
16/11732-0 - Singularities of smooth function germs, BP.IC
15/25191-9 - The Euler obstruction and generalizations, BP.DR
16/02701-4 - Flat and round singularity theory, BE.PQ
16/10580-2 - Basic Mathematics for Aeronautical Engineering, BP.IC
15/12667-5 - Lipschitz geometry of tame singular sets and mappings, BP.PD
15/16746-7 - Equisingularity and the theory of integral closure of modules, BE.PQ
15/07612-7 - Uniform isochronous centers in planar polynomial differential systems of degree 5, BP.PD
15/08026-4 - Bilipschitz geometry and surface singularities resolution, BP.PD
15/08149-9 - Variations in multiplicities and limited polynomials, BP.PD
15/05380-1 - Introduction to the singularity theory of differentiable maps, BP.IC
15/02102-0 - An introduction to singularity theory, BP.IC
15/04807-1 - Functions in complex variables, BP.IC - associated scholarships

Abstract

Singularity theory has wide applications to various areas of mathematics and in particular to differential geometry and qualitative theory of differential equations. These branches of mathematics feedback, in turn, into and enrich singularity theory. The aim of this project is to develop methods of classification of real and complex singularities with special attention to invariants and equisingularity conditions for families of sets and mappings, and to apply singularity theory to problems in differential geometry and differential equations. The project, with well defined objectives, aims at consolidating research activities in the state of São Paulo in geometric aspects of dynamical systems and singularity theory. The interaction will promote the development in the following areas: 1) geometry and classification of singularities; 2) topology of singular sets and mappings; 3) algebraic methods in singularity theory; 4) singularities in differential geometry; 5) applications to bifurcation problems and to the qualitative theory of differential equations. (AU)

Scientific publications (39)
(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)
EYRAL, CHRISTOPHE; SOARES RUAS, MARIA APARECIDA. On the Zariski multiplicity conjecture for weighted homogeneous and Newton nondegenerate line singularities. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 30, n. 11 OCT 2019. Web of Science Citations: 0.
BENEDINI RIUL, P.; RUAS, M. A. S.; OSET SINHA, R. THE GEOMETRY OF CORANK 1 SURFACES IN R-4. QUARTERLY JOURNAL OF MATHEMATICS, v. 70, n. 3, p. 767-795, SEP 2019. Web of Science Citations: 0.
BRANDER, DAVID; TARI, FARID. Families of spherical surfaces and harmonic maps. Geometriae Dedicata, v. 201, n. 1, p. 203-225, AUG 2019. Web of Science Citations: 0.
BRUCE, J. W.; TARI, F. Frame and direction mappings for surfaces in R-3. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v. 149, n. 3, p. 795-830, JUN 2019. Web of Science Citations: 0.
RODRIGUES HERNANDES, M. E.; RUAS, M. A. S. Parametrized monomial surfaces in 4-space. QUARTERLY JOURNAL OF MATHEMATICS, v. 70, n. 2, p. 473-485, JUN 2019. Web of Science Citations: 0.
AHMED, IMRAN; SOARES RUAS, MARIA APARECIDA. Determinacy of determinantal varieties. MANUSCRIPTA MATHEMATICA, v. 159, n. 1-2, p. 269-278, MAY 2019. Web of Science Citations: 0.
GAFFNEY, TERENCE; GRULHA, JR., NIVALDO G.; RUAS, MARIA A. S. The local Euler obstruction and topology of the stabilization of associated determinantal varieties. MATHEMATISCHE ZEITSCHRIFT, v. 291, n. 3-4, p. 905-930, APR 2019. Web of Science Citations: 0.
RUAS, M. A. S.; SILVA, O. N. Whitney equisingularity of families of surfaces in C-3. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, v. 166, n. 2, p. 353-369, FEB 2019. Web of Science Citations: 0.
LLIBRE, JAUME; OLIVEIRA, REGILENE D. S.; VALLS, CLAUDIA. Final evolutions for simplified multistrain/two-stream model for tuberculosis and dengue fever. CHAOS SOLITONS & FRACTALS, v. 118, p. 181-186, JAN 2019. Web of Science Citations: 0.
BRASSELET, JEAN-PAUL; MIWA LIBARDI, ALICE KIMIE; RIZZIOLLI, ELIRIS CRISTINA; SAIA, MARCELO JOSE. Cobordism of maps of locally orientable Witt spaces. PUBLICATIONES MATHEMATICAE-DEBRECEN, v. 94, n. 3-4, p. 299-317, 2019. Web of Science Citations: 0.
THUY, NGUYEN THI BICH; RUAS, MARIA APARECIDA SOARES. ON SINGULAR VARIETIES ASSOCIATED TO A POLYNOMIAL MAPPING FROM C-n TO Cn-1. ASIAN JOURNAL OF MATHEMATICS, v. 22, n. 6, p. 1157-1171, DEC 2018. Web of Science Citations: 0.
FERNANDES, WILKER; OLIVEIRA, REGILENE; ROMANOVSKI, VALERY G. Isochronicity of a Z(2)-equivariant quintic system. Journal of Mathematical Analysis and Applications, v. 467, n. 2, p. 874-892, NOV 15 2018. Web of Science Citations: 0.
KERNER, DMITRY; PEDERSEN, HELGE MOLLER; RUAS, MARIA A. S. Lipschitz normal embeddings in the space of matrices. MATHEMATISCHE ZEITSCHRIFT, v. 290, n. 1-2, p. 485-507, OCT 2018. Web of Science Citations: 2.
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.
OSET SINHA, RAUL; TARI, FARID. ON THE FLAT GEOMETRY OF THE CUSPIDAL EDGE. OSAKA JOURNAL OF MATHEMATICS, v. 55, n. 3, p. 393-421, JUL 2018. Web of Science Citations: 3.
LLIBRE, JAUME; OLIVEIRA, REGILENE. Quadratic systems with an invariant conic having Darboux invariants. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, v. 20, n. 4 JUN 2018. Web of Science Citations: 0.
LLIBRE, JAUME; OLIVEIRA, REGILENE; RODRIGUES, CAMILA AP B. On the periodic solutions of the Michelson continuous and discontinuous piecewise linear differential system. COMPUTATIONAL & APPLIED MATHEMATICS, v. 37, n. 2, p. 1550-1561, MAY 2018. Web of Science Citations: 0.
MARTINEZ-ALFARO, JOSE; MEZA-SARMIENTO, INGRID S.; OLIVEIRA, REGILENE D. S. SINGULAR LEVELS AND TOPOLOGICAL INVARIANTS OF MORSE-BOTT FOLIATIONS ON NON-ORIENTABLE SURFACES. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 51, n. 1, p. 183-213, MAR 2018. Web of Science Citations: 0.
LLIBRE, JAUME; OLIVEIRA, REGILENE; VALLS, CLAUDIA. Phase portraits for some symmetric Riccati cubic polynomial differential equations. Topology and its Applications, v. 234, p. 220-237, FEB 1 2018. Web of Science Citations: 0.
DIAS, FABIO SCALCO; TARI, FARID. ON VERTICES AND INFLECTIONS OF PLANE CURVES. JOURNAL OF SINGULARITIES, v. 17, p. 70-80, JAN-DEC 2018. Web of Science Citations: 0.
MENCINGER, MATEJ; FERCEC, BRIGITA; FERNANDES, WILKER; OLIVEIRA, REGILENE. Linearizability problem of persistent centers. Electronic Journal of Qualitative Theory of Differential Equations, n. 37, p. 1-27, 2018. Web of Science Citations: 1.
HASEGAWA, MASARU; TARI, FARID. On Umbilic Points on Newly Born Surfaces. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 48, n. 4, p. 679-696, DEC 2017. Web of Science Citations: 0.
SALARINOGHABI, MOSTAFA; TARI, FARID. FLAT AND ROUND SINGULARITY THEORY OF PLANE CURVES. QUARTERLY JOURNAL OF MATHEMATICS, v. 68, n. 4, p. 1289-1312, DEC 2017. Web of Science Citations: 2.
OLIVEIRA, REGILENE D. S.; REZENDE, ALEX C.; SCHLOMIUK, DANA; VULPE, NICOLAE. GEOMETRIC AND ALGEBRAIC CLASSIFICATION OF QUADRATIC DIFFERENTIAL SYSTEMS WITH INVARIANT HYPERBOLAS. Electronic Journal of Differential Equations, NOV 28 2017. Web of Science Citations: 2.
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.
BRASSELET, JEAN-PAUL; CHACHAPOYAS, NANCY; RUAS, MARIA A. S. Generic sections of essentially isolated determinantal singularities. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 28, n. 11 OCT 2017. Web of Science Citations: 3.
ROMANOVSKI, VALERY G.; FERNANDES, WILKER; OLIVEIRA, REGILENE. Bi-center problem for some classes of Z(2)-equivariant systems. Journal of Computational and Applied Mathematics, v. 320, p. 61-75, AUG 15 2017. Web of Science Citations: 5.
REEVE, GRAHAM MARK; TARI, FARID. MINKOWSKI SYMMETRY SETS OF PLANE CURVES. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 60, n. 2, p. 461-480, MAY 2017. Web of Science Citations: 0.
BARBOSA, G. F.; GRULHA, JR., N. G.; SAIA, M. J. Minimal Whitney stratification and Euler obstruction of discriminants. Geometriae Dedicata, v. 186, n. 1, p. 173-180, FEB 2017. Web of Science Citations: 1.
LLIBRE, JAUME; OLIVEIRA, REGILENE; VALLS, CLAUDIA. On the Darboux integrability of a three-dimensional forced-damped differential system. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, v. 24, n. 4, p. 473-494, 2017. Web of Science Citations: 1.
OLIVEIRA, REGILENE; VALLS, CLAUDIA. Polynomial integrability of Hamiltonian systems with homogeneous potentials of degree -k. Physics Letters A, v. 380, n. 46, p. 3876-3880, DEC 1 2016. Web of Science Citations: 0.
REMIZOV, A. O.; TARI, F. Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics. Geometriae Dedicata, v. 185, n. 1, p. 131-153, DEC 2016. Web of Science Citations: 4.
ARTES, JOAN C.; OLIVEIRA, REGILENE D. S.; REZENDE, ALEX C. Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple Saddle. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 26, n. 11 OCT 2016. Web of Science Citations: 0.
NISHIMURA, T.; OSET SINHA, R.; RUAS, M. A. S.; WIK ATIQUE, R. Liftable vector fields over corank one multigerms. MATHEMATISCHE ANNALEN, v. 366, n. 1-2, p. 573-611, OCT 2016. Web of Science Citations: 1.
DIAS, FABIO SCALCO; TARI, FARID. ON THE GEOMETRY OF THE CROSS-CAP IN MINKOWSKI 3-SPACE AND BINARY DIFFERENTIAL EQUATIONS. TOHOKU MATHEMATICAL JOURNAL, v. 68, n. 2, p. 293-328, JUN 2016. Web of Science Citations: 2.
OLIVEIRA, REGILENE; VALLS, CLAUDIA. Chaotic Behavior of a Generalized Sprott E Differential System. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 26, n. 5 MAY 2016. Web of Science Citations: 0.
OLIVEIRA, REGILENE; VALLS, CLAUDIA. Global dynamical aspects of a generalized Chen-Wang differential system. NONLINEAR DYNAMICS, v. 84, n. 3, p. 1497-1516, MAY 2016. Web of Science Citations: 0.
EYRAL, CHRISTOPHE; RUAS, MARIA APARECIDA SOARES. TOPOLOGICAL TRIVIALITY OF LINEAR DEFORMATIONS WITH CONSTANT LE NUMBERS. KODAI MATHEMATICAL JOURNAL, v. 39, n. 1, p. 189-201, MAR 2016. Web of Science Citations: 1.
MARTINEZ-ALFARO, J.; MEZA-SARMIENTO, I. S.; OLIVEIRA, R. D. S. Singular levels and topological invariants of Morse Bott integrable systems on surfaces. Journal of Differential Equations, v. 260, n. 1, p. 688-707, JAN 5 2016. Web of Science Citations: 2.

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