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Protégé : PR et MCF invités 2011-2012 à l’IMT

11/07/2011 Comments off

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Master 2

06/07/2011 Comments off

Introduction aux systèmes intégrables

tous les mercredi de 9h à 12h salle 131 bât 1R2

première séance le 12 Octobre

programme (11 cours)
  1. La Mécanique de Lagrange. Exemples.
  2. Transformation de Legendre: enveloppes, courbes polaires. Equation de Hamilton.
  3. Mécanique lagrangienne et hamiltonienne sur une variété. Variétés symplectiques.
  4. Flots hamiltoniens et transformations symplectiques. L’algèbre de Lie de champs de vecteurs. Groupes de Lie.
  5. Représentation adjointe d’un groupe et d’une algèbre de Lie:  Ad et ad. L’algèbre de Lie des fonctions de Hamilton.
  6. Théorèmes de Liouville, Frobenius, Noether. Méthode de Hamilton-Jacobi d’intégration. Exemples.
  7. Structure de Poisson. Structure de Poisson canonique sur le dual d’une algèbre de Lie. Action co-adjointe, flot Hamiltonien.
  8. Orbites co-adjointes et leur structure symplectique. Identification d’une algèbre avec son dual, paires de Lax et champs Hamiltoniens. Exemple: équations d’Euler-Poisson sur e(3). (semaine du 28 novembre)
  9. R-matrice, thérème AKS, système de Toda.
  10. Système de Calogero-Moser.

Littérature

GEOMETRIE DIFFERENTIELLE, C. Doss-Bachelet, J.-P. Françoise, C. Piquet, Ellipses, Paris, 2000.

MATHEMATICAL METHODS OF THE CLASSICAL MECHANICS, Springer, V.I. Arnold

INTRODUCTION TO CLASSICAL INTEGRABLE SYSTEMS
O. Babelon, D. Bernard, M. Talon. November 21, 2000
http://catdir.loc.gov/catdir/samples/cam033/2002034955.pdf
http://gen.lib.rus.ec/get?md5=f6cbd1f7d7bcd6ae8c2dde08fc7b16ed

A SHORT INTRODUCTION TO CLASSICAL AND QUANTUM INTEGRABLE SYTEMS. O. Babelon
Université Paris 6; CNRS; Université Paris 7; 2007
http://www.lpthe.jussieu.fr/~babelon/saclay2007.pdf

SPINNING TOPS, M. Audin, Cambridge University Press, 1996.

INTEGRABLE SYSTEMS OF CLASSICAL MECHANICS AND LIE ALGEBRAS, A. M. Perelomov, Birkhauser, 1990.

Sujet de l’examen du 20 janvier 2012 ici

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Ancienne page de mes enseignements

04/07/2011 Comments off

http://www.math.univ-toulouse.fr/~gavrilov/enseignement/enseignement.html

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Publications

04/07/2011 Comments off

[1] On the integrable cases of the equations of heavy gyrostat (in russian), L.Gavrilov, Annuaire de l’Université de Sofia, Mecanique, vol.80 (1986).

[2] Invariant asymptotic stable tori in the perturbed sine-Gordon equation, L.Gavrilov, Serdica, vol.13 (1987) 26-51.

[3] Explicit solutions of Gorjatchev-Tchaplygin top, L.Gavrilov, Compt.Rend.Acad.Bulg.Sci., vol.40, No 4, 19-22 (1987).

[4] On the Geometry of Gorjatchev-Tchaplygin top, L.Gavrilov, Compt.Rend.Acad.Bulg.Sci., vol. 40, No 9, 33-36 (1987).

[5] Non-integrability of a class of differential equations which are not of Painleve type, L.Gavrilov, Compt.Rend.Acad.Bulg.Sci., vol. 41, No 3, 21-24 (1988).

[6] Note on the generalized Henon-Heiles system, L.Gavrilov, Compt.Rend.Acad.Bulg.Sci., vol. 41, No 8, 29-32 (1988).

[7] Bifurcations of invariant manifolds in the generalized Henon-Heiles system, L.Gavrilov, Physica D34, 223-239 (1989).

[8] Remarks on the equations of heavy gyrostat, L.Gavrilov, Compt.Rend.Acad.Bulg.Sci., vol. 42, No 5, 17-20 (1989).

[9] A Lax pair for the generalized Henon-Heiles system, L.Gavrilov, 7th Czechoslovak Copnference on Differential Equations and Their Applications EQUADIFF7, Abstracts I, p.67, Praha 1989.

[10] Non-integrability of the equations of heavy gyrostat, L.Gavrilov, Compositio Mathematica, vol. 82 (1992) 275-291.

[11] Limit cycles and zeroes of Abelian integrals satisfying third order Picard-Fuchs equations, L.Gavrilov, E.Horozov, in J.-P. Franoise and R. Roussarie (Eds), Bifurcations of Planar Vector Fields, Lecture Notes in Mathematics, vol.1455, 160-186, Springer-Verlag, 1990.

[12] Remark on the number of critical points of the period, L. Gavrilov, J. Differential Equations,  101 (1993) 58-65.

[13] Limit cycles of perturbations of quadratic Hamiltonian vector fields, L.Gavrilov, E.Horozov, J. de Mathématiques Pures et Appliquées, 72,1993, 213 – 238.

[14] Bi-Hamiltonian structure of an integrable Hnon-Heiles system, R.Caboz, V.Ravoson, L.Gavrilov, J. Physics A: Math.Gen. 24 (1991) L523-L525.

[15] Bifurcations des tores de Liouville du potentiel de Kolosoff U = r + 1/r – k.cos(j), L.Gavrilov, M.Ouazzani-Jamil, R.Caboz,
C.R.Acad.Sci. Paris, t. 315, Serie I, p.289-294, 1992.

[16] Bifurcation diagrams and Fomenko’s surgery on Liouville tori of the Kolossof potential U= r + 1/r – k.cos(j), L.Gavrilov, M.Ouazzani-Jamil, R.Caboz,
Annales Sci. de l’Ecole Norm. Sup., 4e serie, 26,1993, 545 – 564.

[17] The period function of a Hamiltonian quadratic system, W.A. Coppel, L.Gavrilov, Integral and Differential Equations, 6 (1993) 1357-1365.

[18] Separability and Lax pairs for Hnon – Heiles system, V.Ravoson, L.Gavrilov, R.Caboz, J.Math.Physics 34, No 6, p.2385-2393,1993.

[19] On the topology of polynomials in two complex variables, preprint No 45, Laboratoire de Topologie et Gometrie, UPS, Toulouse, 1994 (non-published).

[20] Isochronism of plane polynomial hamiltonian systems, L.Gavrilov, Nonlinearity 10 (1997) 433-448.

[21] The complex geometry of Lagrange top, L.Gavrilov, A. Zhivkov, l’Enseignement Mathematique, 44 (1998) 133-17.

[22] Generalized Jacobians of spectral curves and completely integrable systems, L.Gavrilov, Math. Zeitschrift, 230, 487-508 (1999)

[23] Integrable systems and algebraic groups, L.Gavrilov, in J.Chavarriga, J.Gin (Eds), Proc.of 3th Catalan Days of Applied Math., p.81-92, Lleida, Spain, 1996.

[24] Petrov modules and zeros of Abelian integrals, L.Gavrilov, Bull. des Sciences Math., 122 (1998) 571-584.

[25] Nonoscillation of elliptic integrals related to cubic polynomials with symmetry of order three, L.Gavrilov, Bull. London Math. Soc., 30 (1998) 267-273.

[26] The real period function of A3 singularity, L.Gavrilov, O. Vivolo, Comp. Mathematica 123 (2000), no. 2, 167–184

[27] Modules of Abelian integrals, L. Gavrilov, Proc.of 4th Catalan Days of Applied Math., p.35-46, Tarragona, Spain, 1998.

[28] Abelian integrals related to Morse polynomials and perturbations of plane Hamiltonian vector fields, L. Gavrilov, Annales de l’Institut Fourier  49 (1999) 611-652.

[29] Second order analysis in polynomially perturbed reversible quadratic vector fields, L. Gavrilov, I.D. Iliev, Erg. Theory & Dyn. Systems, (2000), 20, 1671-1686.

[30] On the explicit solutions of the elliptic Calogero system, L. Gavrilov, A.Perelomov, J. Math. Physics, 40 (1999),  no. 12, 6339–6352.

[31] The infinitesimal 16th Hilbert problem in the quadratic case, L. Gavrilov, Invent. Math. 143, 449-497 (2001).

[32] Bifurcations of limit cycles from infinity in quadratic systems, L. Gavrilov, I.D. Iliev,  Canadian J. Math.   54  (2002) 1038-1064.

[33] Jacobians of singularized spectral curves and completely integrable systems, L. Gavrilov,  in « Kovalevski property », CRM Proceedings and Lectures Notes, Vol. 32, 59-68 (2002), AMS, Ed. V. Kuznetsov.

[34] Two dimensional Fuchsian systems and the Chebishev property, L. Gavrilov, I.D. Iliev,  J. Diff. Eqns. , 191 (2003) 105-120.

[35] Complete hyperelliptic integrals of the first kind and their non-oscillation, L. Gavrilov, I.D. Iliev,  Trans. Amer. Math. Soc. 356 (2004), 1185-1207.

[36] The displacement map associated to polynomial unfoldings of planar Hamiltonian vector fields, L. Gavrilov, I.D. Iliev,  American J. of Math., 127 (2005) 1153-1190.

[37] Higher order Poincare-Pontryagin functions and iterated path integrals, L. Gavrilov,  Ann. Fac. Sci. Toulouse Math. (6) 14 (2005), no. 4, pp. 663-682.

[38] Families of Painlevé VI  equations having a common solution, Bassem Ben Hamed, Lubomir Gavrilov,
Intern. Math. Res. Notes  vol. 60 (2005) 3727-3752. e-reprints link

[39] The infinitesimal 16th Hilbert problem in dimension zero, L. Gavrilov, H. Movasati, Bull. Sci. math. 131 (2007) 242–257.

[40] Perturbations of quadratic centers of genus one, S. Gautier, L. Gavrilov, Iliya D. Iliev, Discrete Contin. Dyn. Syst. 25 (2009), no. 2, 511–535.

[41] Cyclicity of period annuli and principalization of Bautin ideals, L. Gavrilov, Ergodic Theory Dynam. Systems 28 (2008), no. 5, 1497–1507.

[42] On the cyclicity of weight-homogeneous centers, L. Gavrilov, J. Gine, M. Grau, J. Differential Equations 246 (2009) 3126-3135.

[43] On the non-persistence of Hamiltonian identity cycles, L. Gavrilov, H. Movasati, I. Nakai , J. Differential Equations 246 (2009) 2706–2723.

[44] On the finite cyclicity of open period annuli, L. Gavrilov, D. Novikov,  Duke Math. J. 152 (2010), no. 1, 1–26

[45] Quadratic perturbations of codimension-four quadratic centers, L. Gavrilov, Iliya D. Iliev, J. Math. Anal. Appl. 357 (2009) 69-76.

[46] On the number of limit cycles which appear by perturbation of Hamiltonian two-saddle cycles of planar vector fields, L. Gavrilov, Bull Braz Math Soc, New Series 42 (2011), no. 1, 1-23.

[47] On the reduction of the degree of linear differential operators, Marcin Bobieński and Lubomir Gavrilov, Nonlinearity 24 (2011) 373-388.

[48] The holonomy group at infinity of the Painlevé VI Equation, B. Ben Hamed, L. Gavrilov and M. Klughertz
J. Math. Phys. 53, 022701 (2012)

[49] Moments on Riemann surfaces and hyperelliptic Abelian integrals, L. Gavrilov, F. Pakovich,   Comment. Math. Helv.   89, Issue 1, 2014, pp. 125–155

[50] Perturbations of quadratic Hamiltonian two-saddle cycles, L. Gavrilov, I.D. Iliev,   Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015) 307–324 http://arxiv.org/abs/1306.2340

[51] On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields, Lubomir Gavrilov, Functional Analysis and Its Applications, Volume 47 (2013), Issue 3, pp 174-186.

[52] Finite cyclicity of quadratic slow-fast Darboux systems with a two-saddle loop, Marcin Bobieński and Lubomir Gavrilov, Proc. Amer. Math. Soc. 144 (2016), 4205-4219.

[53] Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain, Bassem Ben Hamed, Ameni Gargouri, Lubomir Gavrilov, J. Math. Anal. Appl. 424 (2015), no. 1, 774–784.

[54] Cubic perturbations of elliptic Hamiltonian vector fields of degree three, L. Gavrilov, I.D. Iliev,  J. of Diff. Equations   260 (2016)  3963–3990 http://arxiv.org/abs/1406.0208

[55] Cubic Perturbations of Symmetric elliptic Hamiltonians of degree four in a Complex domain, Bassem Ben Hamed, Ameni Gargouri, Lubomir Gavrilov, Bull. des Sciences Math, vol.157, December 2019, 102796. 

[56]  Irreducibility of the Picard-Fuchs equation related to the Lotka-Volterra polynomial x^2y^2(1−x−y), L. Gavrilov,  J. Dyn. Control Syst. 24 (2018), no. 3, 425–438 https://doi.org/10.1007/s10883-017-9379-2          https://arxiv.org/abs/1612.09560

[57] Hilbert’s 16th problem on a period annulus and Nash space of arcs,  L. Gavrilov, J.-P. Françoise, D. Xiao,  

Math. Proc. Camb. Philos. Soc. 169, No. 2, 377-409 (2020).

[58] On the center-focus problem for theAbel equation Annales Henri Lebesgue, Volume 3 (2020) , pp. 615-648

extended version of two lectures given during the  Zagreb Dynamical Systems Workshop, October 22-26, 2018.

https://arxiv.org/abs/1811.10506

[59] Special cubic perturbations of the Duffing oscillator x′′ = x − x^3 near the eight-loop, Bassem Ben Hamed, Ameni Gargouri, Lubomir Gavrilov, Mediterr. J. Math. 18, 229 (2021). https://doi.org/10.1007/s00009-021-01868-5

[60] Centers of reversible cubic perturbations of the symmetric 8-loop Hamiltonian, Sassi, F., Gargouri, A., Gavrilov, L. et al.  Archiv der Mathematik 115, pages 567–574 (2020)

[61] Perturbation theory of the quadratic Lotka-Volterra double center, L. Gavrilov, J.-P. Françoise, Commun. Contemp. Math., 24(5):38, 2022.  

[62] The limit cycles in a generalized Rayleigh-Liénard oscillator, L. Gavrilov, I. D. Iliev, Discrete and Continuous Dynamical Systems Vol. 43, No. 6, June 2023, pp. 2381-2400

[63] Smooth points of the space of plane foliations with a center, L. Gavrilov, H. Movasati, International Mathematics Research Notices, Vol. 2023,No. 15,pp. 13477–13500.

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articles non-mathématiques (bulgare)

03/07/2011 Comments off

Пропорционална изборна система с централна листа, Любомир Гаврилов и  Стефан Манов

КЪM НОВО ИЗБОРНО ЗАКОНОДАТЕЛСТВО ? част първа : Анатомия на гласуването в чужбина, проф. Любомир Гаврилов и д-р Стефан Mанов, Mediapool.bg, 4 Ноември 2009 и сп.“Общество и право“, бр. 10/2009г.

КЪM НОВО ИЗБОРНО ЗАКОНОДАТЕЛСТВО ? Част втора : Изборна География, проф. Любомир Гаврилов и д-р Стефан Mанов, сп.“Общество и право“, бр. 8/2010 г., pdf, Eurochicago, сп. Капитал

Институционално представителство на диаспората. Френският модел, Любомир Гаврилов и Стефан Mанов, сп. Правен Свят бр. 10 / 2011, http://www.legalworld.etaligent.net/show.php?storyid=27638

Имат ли права външните българи?,  Култура – Брой 31 (2693), 21 септември 2012, http://www.kultura.bg/bg/article/view/20084

Пресметни си сам резултатите от Парламентарни избори 2013, Програма за пресмятане на крайните резултати от изборите с отворен код на Javascript, работеща в браузърите IE10+, Firefox 20+, Chrome 23+, Opera 12.10+, Safari 5.1+. проф. Любомир Гаврилов, Институт по математика, Тулуза (математически анализ),  д-р Стефан Манов (концепция и алгоритъм) , Делян Делчев (програмиране) https://www.bivol.bg/bg-elections-code.html

Администратор съм на следните блогове:

Проектът ИЗБОРЕН КОДЕКС, Целта на този блог е да представи експертен проект за подобряване на съществуващия Изборен Кодекс, с подкрепата на „Временните обществени съвети на българите в чужбина“, „Френско-Български Форум“ и други български организации в чужбина. Анализира се изборното законодателство в редица европейски държави, както и международния опит свързан с гласуването по Интернет.

Българо-Френски Форум, блог на българската общност и на приятелите на България в Тулуза и региона

Обществени съвети на българите в чужбина, блог на българите без граници

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