Publications

gavrilov — Mon, 04 Jul 2011 00:00:11 +0000

[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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Publications