Instituto de Investigación
en Matemáticas

Ecuaciones y Singularidades

(ECSING)


Objetivos: El grupo investigador ECSING trabaja en investigación básica en matemáticas, en todas sus facetas, con ramificaciones al desarrollo aplicado y acento en la formación de investigadores. Los objetivos son continuación de los objetivos básicos que viene persiguiendo nuestro equipo desde hace ya más de quince años, soportado por diferentes contratos nacionales y europeos. Las razones son esencialmente las mismas del inicio. Señalaremos no obstante una evolución hacia la geometría moderada, debido a los resultados de J.M. Lion y de la escuela de lógicos, un refuerzo del papel de la teoría de valoraciones, en relación también con el caso real de cuerpos de Hardy, una línea nueva de topología de sistemas dinámicos que promete más resultados, el desembarco de J. Ribón en el estudio de sistemas dinámicos discretos, sobre lo que por el momento es nuestro único especialista, así como una vuelta a temas clásicos como el de las polares, con la nueva óptica de los sistemas dinámicos. La influencia de Ramis y Malgrange asimismo está relanzando la Teorís de Galois diferencial, con una versión no lineal en la que deseamos entrar y para la que contamos con Aroca, Mozo y J. Cano. Los algoritmos obtenidos por F. Aroca y J. Cano nos acercan también a los resultados aplicados.
Líneas de investigación: Teoría de Galois de ecuaciones diferenciales. Geometría y topología de campos de vectores. Construcción explícita de soluciones de ODEs y EDPs. Foliaciones holomorfas singulares. Clasificación de difeomorfismos en varias variables. Desarrollos asintóticos. Reducción de singularidades.
Publicaciones:
Absolutely isolated singularities of holomorphic vector fields Invent. Math. 98 351--369 (1989) Camacho, C. and Cano, F. and Sad, P.
Réduction des singularitiés des feuilletages holomorphes C. R. Acad. Sci. Paris Sér. I Math. 307 795--798 (1988) Cano, Felipe
Le probl`eme de la séparatrice: une conséquence de la réduction des singularités de feuilletages C. R. Acad. Sci. Paris Sér. I Math. 307 387--390 (1988) Cano, Felipe and Cerveau, Dominique
Local and global results on the desingularization of three-dimensional vector fields Astérisque 0 15--58, 185 (1987) Cano, F.
Final forms for a three-dimensional vector field under blowing-up Ann. Inst. Fourier (Grenoble) 37 151--193 (1987) Cano, Felipe
Desingularizations of plane vector fields Trans. Amer. Math. Soc. 296 83--93 (1986) Cano, F.
Reduction of the singularities of nondicritical singular foliations. Dimension three Amer. J. Math. 115 509--588 (1993) Cano, Felipe
Desingularization of nondicritical holomorphic foliations and existence of separatrices Acta Math. 169 1--103 (1992) Cano, F. and Cerveau, D.
Hypersurfaces intégrales des feuilletages holomorphes Ann. Inst. Fourier (Grenoble) 42 49--72 (1992) Cano, F. and Mattei, J.-F.
Singular foliations of toric type Ann. Fac. Sci. Toulouse Math. (6) 8 45--52 (1999) Camacho, Maria Isabel Tavares and Cano, Felipe
Fronti`ere dúne hypersurface pfaffienne Ann. Sci. 'Ecole Norm. Sup. (4) 28 591--646 (1995) Cano, F. and Lion, J.-M. and Moussu, R.
Reduction of the singularities of codimension one singular foliations in dimension three Ann. of Math. (2) 160 907--1011 (2004) Cano, Felipe
Pinceaux de courbes intégrales dún champ de vecteurs analytique Astérisque 0 1--34 (2004) Cano, Felipe and Moussu, Robert and Sanz, Fernando
Characteristic exponents of semialgebraic singularities Math. Nachr. 276 23--30 (2004) Birbrair, Lev and Cano, Felipe
Holomorphic foliations desingularized by punctual blow-ups J. Pure Appl. Algebra 178 235--243 (2003) Cano, F. and Cerveau, D. and Scárdua, B.
Topological equivalence for multiple saddle connections An. Acad. Brasil. Ci^enc. 74 577--584 (2002) Alonso, Clementa and Camacho, Maria Izabel and Cano, Felipe
Pinceau intégral enlacé C. R. Math. Acad. Sci. Paris 334 855--858 (2002) Cano, Felipe and Moussu, Robert and Sanz, Fernando
Oscillation, spiralement, tourbillonnement Comment. Math. Helv. 75 284--318 (2000) Cano, F. and Moussu, R. and Sanz, F.
Présentation ['Equations différentielles et singularités. En l'honneur de J. M. Aroca] Astérisque 0 vii--ix (2009) Cano, F. and Loray, F. and Morales-Ruiz, J. J. and Spivakovsky, M. and Sad, P.
Parabolic curves for diffeomorphisms in $Bbb C^2$ Publ. Mat. 52 189--194 (2008) Brochero Martínez, F. E. and Cano, F. and López-Hernanz, L.
Topological invariants for singularities of real vector fields in dimension three Discrete Contin. Dyn. Syst. 20 823--847 (2008) Alonso-González, C. and Camacho, M. I. and Cano, F.
Nonoscillating projections for trajectories of vector fields J. Dyn. Control Syst. 13 173--176 (2007) Cano, F. and Moussu, R. and Sanz, F.
Dicritical logarithmic foliations Publ. Mat. 50 87--102 (2006) Cano, Felipe and Corral, Nuria
Invariants topologiques des singularités de champs réels C. R. Math. Acad. Sci. Paris 342 955--958 (2006) Alonso-González, Clementa and Camacho, Izabel and Cano, Felipe
Topological classification of multiple saddle connections Discrete Contin. Dyn. Syst. 15 395--414 (2006) Alonso-González, C. and Camacho, M. I. and Cano, F.
Non-oscillating integral curves and valuations J. Reine Angew. Math. 582 107--141 (2005) Cano, F. and Moussu, R. and Rolin, J.-P.
Infinitesimal Poincaré-Bendixson problem in dimension 3 Int. Math. Res. Not. IMRN 0 5994--6019 (2014) Alonso-González, C. and Cano, F. and Rosas, R.
Reduction of singularities of three-dimensional line foliations Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 108 221--258 (2014) Cano, F and Roche, C. and Spivakovsky, M.
Absolutely dicritical foliations Int. Math. Res. Not. IMRN 0 1926--1934 (2011) Cano, Felipe and Corral, Nuria
Local Brunella's alternative {II}. Partial separatrices Int. Math. Res. Not. IMRN 0 12840--12876 (2015) Cano, Felipe and Ravara-Vago, Marianna
Local Brunella's alternative I. {RICH} foliations Int. Math. Res. Not. IMRN 0 2525--2575 (2015) Cano, Felipe and Ravara-Vago, Marianna and Soares, Márcio
Topological equivalence of holomorphic vector fields with critical singularity Rev. Semin. Iberoam. Mat. Singul. Tordesillas 2 45--56 (1999) Camacho, Maria Izabel
Compounding secret sharing schemes Australas. J. Combin. 30 277--290 (2004) Martínez-Moro, E. and Mozo-Fernández, J. and Munuera, C.
On higher-order Stokes phenomena of an inhomogeneous linear ordinary differential equation J. Comput. Appl. Math. 169 235--246 (2004) Olde Daalhuis, A. B.
Hermitian metrics inducing the Poincaré metric, in the leaves of a singular holomorphic foliation by curves Trans. Amer. Math. Soc. 356 2963--2988 (2004) Lins Neto, A. and Canille Martins, J. C.
Formal power series solutions in a parameter J. Differential Equations 190 559--578 (2003) Sibuya, Yasutaka
Transversely projective structures on a transversely holomorphic foliation. {II} Conform. Geom. Dyn. 6 61--73 (electronic) (2002) Biswas, Indranil
On holomorphic foliations without algebraic solutions Experiment. Math. 10 529--536 (2001) Coutinho, S. C. and Ribeiro, Bruno F. M.
Transversely projective structures on a transversely holomorphic foliation Conform. Geom. Dyn. 5 74--80 (electronic) (2001) Biswas, Indranil
La variété des équations surstables Bull. Soc. Math. France 128 497--528 (2000) Wallet, Guy
On generalized surfaces in $(Bbb C^3,0)$ Astérisque 0 261--268 (2009) Fernández-Sánchez, Percy and Mozo-Fernández, Jorge
A class of singular perturbation solutions to semilinear equations of fourth order Appl. Math. Mech. (English Ed.) 30 1455--1460 (2009) Mo, Jia-qi
Hyperasymptotics and hyperterminants: exceptional cases J. Comput. Appl. Math. 233 555--563 (2009) Olde Daalhuis, A. B.
Solutions canards en des points tournants dégénérés Ann. Fac. Sci. Toulouse Math. (6) 16 799--816 (2007) Forget, Thomas
Singularly perturbed solution for third order nonlinear equations with two parameters Anal. Theory Appl. 23 301--306 (2007) Mo, Jiaqi
Ackerberg-O'Malley resonance in boundary value problems with a turning point of any order Commun. Pure Appl. Anal. 6 311--333 (2007) De Maesschalck, P.
On the classification of non-integrable complex distributions Indag. Math. (N.S.) 17 397--406 (2006) Ito, Toshikazu and Scárdua, Bruno
Borel summability of divergent solutions for singularly perturbed first-order ordinary differential equations Tohoku Math. J. (2) 58 237--258 (2006) Hibino, Masaki
On the quasi-ordinary cuspidal foliations in $(Bbb C^3,0)$ J. Differential Equations 226 250--268 (2006) Fernández-Sánchez, Percy and Mozo-Fernández, Jorge
Algebraic reduction theorem for complex codimension one singular foliations Comment. Math. Helv. 81 157--169 (2006) Cerveau, Dominique and Lins-Neto, Alcides and Loray, Frank and Pereira, Jorge Vitório and Touzet, Frédéric
Topological classification of holomorphic, semi-hyperbolic germs, in ``quasi-absence'' of resonances Math. Ann. 334 609--625 (2006) Giuseppe, Pietro Di
On foliations with rational first integral Proyecciones 24 175--179 (2006) (2005) Licanic, Sergio
Sur les notions de quasi-homogénéité de feuilletages holomorphes en dimension deux Bull. Braz. Math. Soc. (N.S.) 36 177--185 (2005) Marín, David
Virtual turning points and bifurcation of Stokes curves for higher order ordinary differential equations J. Phys. A 38 3317--3336 (2005) Aoki, Takashi and Kawai, Takahiro and Sasaki, Shunsuke and Shudo, Akira and Takei, Yoshitsugu
On codimension one foliations with prescribed cuspidal separatrix J. Differential Equations 256 1702--1717 (2014) Fernández-Sánchez, Percy and Mozo-Fernández, Jorge and Neciosup, Hernán
Strong asymptotic expansions in a multidirection Funkcial. Ekvac. 55 317--345 (2012) Lastra, Alberto and Mozo-Fernández, Jorge and Sanz, Javier
A non generic case of differential system of $Bbb R^3$ Appl. Math. Sci. (Ruse) 6 4955--4964 (2012) Hadadine, Mohamed Zine eddine and Belaib, Lekhmissi
Exponentially accurate solution tracking for nonlinear {ODE}s, the higher order Stokes phenomenon and double transseries resummation Nonlinearity 25 1559--1584 (2012) Howls, C. J. and Olde Daalhuis, A. B.
Geometric properties of the Riemann surfaces associated with the Noumi-Yamada systems with a large parameter J. Math. Soc. Japan 63 1085--1119 (2011) Aoki, Takashi and Honda, Naofumi
On the exact {WKB} analysis of higher order simple-pole type operators Adv. Math. 228 63--96 (2011) Kawai, Takahiro and Koike, Tatsuya and Takei, Yoshitsugu
On the structure of higher order simple-pole type operators in exact {WKB} analysis Funkcial. Ekvac. 53 249--276 (2010) Kawai, Takahiro and Koike, Tatsuya and Takei, Yoshitsugu
Dynamics of separatrices in holomorphic vector fields Miscelánea Mat. 0 77--82 (1999) López López, Jorge Luis
Non-oscillating solutions of analytic gradient vector fields Ann. Inst. Fourier (Grenoble) 48 1045--1067 (1998) Sanz, Fernando
A complex analogue of the Rolle theorem and polynomial envelopes of irreducible differential equations in the complex domain J. London Math. Soc. (2) 56 305--319 (1997) Novikov, D. and Yakovenko, S.
Trajectoires non-oscillantes des champs de vecteurs gradients C. R. Acad. Sci. Paris Sér. I Math. 325 429--432 (1997) Sanz, Fernando
Pinceaux de courbes intégrales dún champ de vecteurs analytique Astérisque 0 1--34 (2004) Cano, Felipe and Moussu, Robert and Sanz, Fernando
Generic and stability properties of reciprocal and pseudogradient vector fields Math. Slovaca 54 349--368 (2004) Kramár, Miroslav
Formal normal forms for the perturbations of a quasi-homogeneous Hamiltonian vector field J. Dynam. Control Systems 10 545--575 (2004) Paul, E.
Analytic integrability and characterization of centers for nilpotent singular points Z. Angew. Math. Phys. 55 725--740 (2004) Giné, Jaume
Solutions of a pair of differential equations and their applications Proc. Japan Acad. Ser. A Math. Sci. 80 1--5 (2004) Yang, Lian-Zhong
An extension of the Poincaré compactification and a geometric interpretation Proyecciones 22 161--180 (2003) Vidal, Claudio and Gómez, Pedro
On the index of a vector field tangent to a hypersurface with non-isolated zero in the embedding space Math. Nachr. 260 48--57 (2003) Klehn, Oliver
On the nonexistence of Laurent polynomial first integrals for general semi-quasihomogeneous systems Northeast. Math. J. 19 193--196 (2003) Shi, Shaoyun and Zhu, Wenzhuang and Huang, Qingdao
Some criteria for the existence of limit cycles for quadratic vector fields J. Math. Anal. Appl. 282 296--304 (2003) Chavarriga, J. and García, I. A.
Balanced coordinates for spiraling dynamics Qual. Theory Dyn. Syst. 3 181--226 (2002) Sanz, Fernando
Tame semiflows for piecewise linear vector fields Ann. Inst. Fourier (Grenoble) 52 1593--1628 (2002) Panazzolo, Daniel
Pinceau intégral enlacé C. R. Math. Acad. Sci. Paris 334 855--858 (2002) Cano, Felipe and Moussu, Robert and Sanz, Fernando
Normal forms near a saddle-node and applications to finite cyclicity of graphics Ergodic Theory Dynam. Systems 22 783--818 (2002) Dumortier, F. and Ilyashenko, Y. and Rousseau, C.
C^one normal et régularités de Kuo-Verdier Bull. Soc. Math. France 130 71--85 (2002) Orro, Patrice and Trotman, David
Champs de vecteurs analytiques et champs de gradients Ergodic Theory Dynam. Systems 22 525--534 (2002) Lion, Jean-Marie and Moussu, Robert and Sanz, Fernando
Gradient vector fields do not generate twister dynamics J. Differential Equations 174 91--100 (2001) Fortuny, P. and Sanz, F.
Invariant curves and topological invariants for real plane analytic vector fields J. Differential Equations 172 212--226 (2001) Risler, Jean-Jacques
Global topological linearization with unbounded nonlinear term Northeast. Math. J. 16 51--60 (2000) Shi, Jin-lin
Projectively Anosov flows with differentiable (un)stable foliations Ann. Inst. Fourier (Grenoble) 50 1617--1647 (2000) Noda, Takeo
Oscillation, spiralement, tourbillonnement Comment. Math. Helv. 75 284--318 (2000) Cano, F. and Moussu, R. and Sanz, F.
On pairs of differential 1-forms in the plane Discrete Contin. Dynam. Systems 6 519--536 (2000) Oliveira, R. D. S. and Tari, F.
Locally definable ^infty G$ manifold structures of locally definable ^rG$ manifolds Far East J. Math. Sci. (FJMS) 35 103--116 (2009) Kawakami, Tomohiro
Gradient horizontal de fonctions polynomiales Ann. Inst. Fourier (Grenoble) 59 1999--2042 (2009) Dinh, Si Tiep and Kurdyka, Krzysztof and Orro, Patrice
Tame functions with strongly isolated singularities at infinity: a tame version of a Parusi'nski's theorem Geom. Dedicata 140 1--17 (2009) Grandjean, Vincent
Rotation of trajectories of Lipschitz vector fields J. Differential Geom. 81 601--630 (2009) Comte, Georges and Yomdin, Yosef
Complex analytic geometry and analytic-geometric categories J. Reine Angew. Math. 626 39--74 (2009) Peterzil, Yaácov and Starchenko, Sergei
Mild manifolds and a non-standard Riemann existence theorem Selecta Math. (N.S.) 14 275--298 (2009) Peterzil, Yaácov and Starchenko, Sergei
Linearization of families of germs of hyperbolic vector fields Dyn. Syst. 23 467--489 (2008) Naudot, Vincent and Yang, Jiazhong
Two parameter families of binary differential equations Discrete Contin. Dyn. Syst. 22 759--789 (2008) Tari, Farid
On the multiplicity of the circumference in planar polynomial vector fields Fixed Point Theory 9 105--137 (2008) Giné, Jaume and Grau, Maite and de Prada, Paz
A first-order version of Pfaffian closure Fund. Math. 198 229--254 (2008) Fratarcangeli, Sergio
Generic singularities of implicit systems of first order differential equations on the plane Jpn. J. Math. 3 93--119 (2008) Davydov, A. A. and Ishikawa, G. and Izumiya, S. and Sun, W.-Z.
Periodic solutions for planar autonomous systems with nonsmooth periodic perturbations J. Math. Anal. Appl. 338 1401--1417 (2008) Makarenkov, Oleg and Nistri, Paolo
Solutions non oscillantes dúne équation différentielle et corps de Hardy Ann. Inst. Fourier (Grenoble) 57 1825--1838 (2007) Blais, Fran{c{c}}ois and Moussu, Robert and Sanz, Fernando
Schlesinger transformations for the second members of {PII} and {PIV} hierarchies J. Phys. A 40 7687--7697 (2007) Sakka, A. H.
The transcendental meromorphic solutions of a certain type of nonlinear differential equations J. Math. Anal. Appl. 334 517--527 (2007) Tang, Jia-Feng and Liao, Liang-Wen
Nonoscillating projections for trajectories of vector fields J. Dyn. Control Syst. 13 173--176 (2007) Cano, F. and Moussu, R. and Sanz, F.
On the limit set at infinity of a gradient trajectory of a semialgebraic function J. Differential Equations 233 22--41 (2007) Grandjean, V.
Bounds for gradient trajectories and geodesic diameter of real algebraic sets Bull. London Math. Soc. 38 951--965 (2006) D'Acunto, D. and Kurdyka, K.
Reducible ordinary differential equations J. Nonlinear Sci. 16 583--613 (2006) Hadeler, K. P. and Walcher, S.
Algebraicity of global real analytic hypersurfaces Geom. Dedicata 119 141--149 (2006) Kucharz, Wojciech and Kurdyka, Krzysztof
Integrability of planar polynomial differential systems through linear differential equations Rocky Mountain J. Math. 36 457--485 (2006) Giacomini, H. and Giné, J. and Grau, M.
On the period function of planar systems with unknown normalizers Proc. Amer. Math. Soc. 134 531--539 (electronic) (2006) Sabatini, M.
Solutions of ''+A(z)f=0$ with prescribed sequences of zeros Acta Math. Univ. Comenian. (N.S.) 74 287--307 (2005) Heittokangas, J. and Laine, I.
Real and complex indices of vector fields on complete intersection curves with isolated singularity Compos. Math. 141 525--540 (2005) Klehn, Oliver
On trajectories of analytic gradient vector fields on analytic manifolds Topol. Methods Nonlinear Anal. 25 167--182 (2005) Nowel, Aleksandra and Szafraniec, Zbigniew
Briot-Bouquet's theorem in high dimension Publ. Mat. 58 135--152 (2014) Carrillo, S. A. and Sanz, F.
On restricted analytic gradients on analytic isolated surface singularities J. Differential Equations 255 1684--1708 (2013) Grandjean, Vincent and Sanz, Fernando
Non-interlaced solutions of 2-dimensional systems of linear ordinary differential equations Proc. Amer. Math. Soc. 141 2429--2438 (2013) Le Gal, O. and Sanz, F. and Speissegger, P.
Derivations and valuation rings Canad. Math. Bull. 56 31--38 (2013) Ayuso, P. Fortuny
Multi-specialization and multi-asymptotic expansions Adv. Math. 232 432--498 (2013) Honda, Naofumi and Prelli, Luca
Periodic solutions of first order systems Discrete Contin. Dyn. Syst. 33 381--389 (2013) Ward, J. R.
On solving systems of autonomous ordinary differential equations by reduction to a variable of an algebra Int. J. Math. Math. Sci. 0 Art. ID 753916, 21 (2012) Alvarez-Parrilla, Alvaro and Frías-Armenta, Martín Eduardo and López-González, Elifalet and Yee-Romero, Carlos
Representative definable ^r$ functions on definable ^r$ groups Bull. Fac. Ed. Wakayama Univ. Natur. Sci. 0 31--34 (2012) Kawakami, Tomohiro
Real logarithmic models for real analytic foliations in the plane Rev. Mat. Complut. 25 109--124 (2012) Corral, Nuria and Sanz, Fernando
Some (non-)elimination results for curves in geometric structures Fund. Math. 214 181--198 (2011) Randriambololona, Serge and Starchenko, Sergei
A definable strong $ retract of a definable $ set in a real closed field Bull. Fac. Ed. Wakayama Univ. Natur. Sci. 0 7--11 (2011) Kawakami, Tomohiro
Algebraic and computational formulas for the index of real analytic vector fields Results Math. 59 125--139 (2011) Castellanos, Víctor and Castorena, Abel and Cruz-López, Manuel
Linearly implicit Liénard systems Nonlinear Anal. 74 213--223 (2011) Riaza, Ricardo
Finding and classifying critical points of 2D vector fields: a cell-oriented approach using group theory Comput. Vis. Sci. 13 377--396 (2010) Effenberger, Felix and Weiskopf, Daniel
Definably complete Baire structures Fund. Math. 209 215--241 (2010) Fornasiero, Antongiulio and Servi, Tamara
Radial index and Poincaré-Hopf index of 1-forms on semi-analytic sets Math. Proc. Cambridge Philos. Soc. 148 297--330 (2010) Dutertre, Nicolas
Quasi-analytic solutions of analytic ODEs and O-minimal Structures Proc. London Math. Soc. 95 413-442 (2007) J.-P. Rolin, R. Schaefcke
Parabolic curves of dieffeomorphisms asymptotic to formal invariant curves Journal für die reine und angewandte Mathematik (Crelle’s Journal) 0 1-19 (2017) L. López, F. Sanz
Local Monomialization of Generalized Analytic Functions RACSAM, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. 107 189-211 (2013) J.-P. Rolin, R. Martín, F. Sanz
Proyectos:
Álgebra y geometría en dinámica real y compleja II
Álgebra y Geometría en Dinámica Real y Compleja III
Álgebra y Geometría en sistemas dinámicos y foliaciones singulares
Otros datos: