Emil Ivanov Horozov

Emil Ivanov Horozov

Professor
DSc
Email: 
horozov@fmi.uni-sofia.bg
Phone: 
+359 2 8161-203
Room: 
FMI-534

Publications

  1. Versal deformations of equivariant vector fields for the cases of symmetry of orders 2 and 3, Trud.sem.I.G.Petrovskogo,  t.1979, Moscow State University, 1979, pp.163-192 (in Russian). (цитирания -- 59)
  2. Bifurcations of  vector fields in a neighborhood of a singular point in the case of two pairs of imaginary eigenvalues. Compt. rend. Acad. bulg. sci. t. 34, 9, 1981, pp.1221-1224 (in Russian).  (цитирания-- 5)
  3.  Bifurcations of  vector fields in a neighborhood of a singular point in the case of two pairs of imaginary eigenvalues.II. Compt. rend. Acad. bulg. sci. t. 35, 2, 1982, pp.149-152 (in Russian).  (цитирания-- 4)
  4.  Bifurcations in some families of the type  $\dot{x}_1={x}_1{f}_1(x,\varepsilon)$, $\dot{x}_2={x}_2{f}_2(x,\varepsilon)$. Compt. rend. Acad. bulg. sci. t. 35, 7, 1982, pp. 889-891(in Russian). (цитирания   -- 1)
  5. On the explicit solutions of C. Neumann's problem describing the motion of a point on the sphere under the action of a
    quadratic potential.Compt. rend. Acad. bulg. sci. t. 37, 2, 1984, pp. 145-148 (in Russian). (цитирания-- 3)
  6. C. Neumann's problem and the equations defining the period matrices of Hyperelliptic Riemann surfaces, Compt. rend. Acad. bulg. sci. t. 37, 3, 1984, pp. 277-280 (in Russian).  (цитирания -- 2)
  7. Collection of problems in ordinary differential equations, University of Sofia, 1984 (in Bulgarian, with G.Karadgov and N. Nikiforov). {цитирания -- 4)
  8. Uniqueness of limit cycles in planar vector fields which leave the axes invariant, Contemp. Math. 56, 1986, pp.117-129 (with St. van Gills). (цитирания --  7)
  9. On the non-integrability of Gross-Neveu models, Ann. Phys., 174, 1987, pp.430-441. (цитирания -- 14)
  10. A Lax pair for the Kowalevski's top, Physica 29 D, 1987, pp.173-180 (with L.Haine).   (цитирания -- 57)
  11. The full geometry of the Kowalevski's top and (1-2)-Abelian varieties, Comm. Pure Appl. Math., v.42,4, 1988 pp.37-407 (with P.van Moerbeke).  (цитирания -- 32)
  12. Perturbations of the spherical pendulum and Abelian integrals,  Jour. reine angew. Math., 408, 1990, pp.114-135. PDF (цитирания -- 49)
  13. Limit cycles and zeros of Abelian integrals satisfying third order Picard-Fuchs equations. In: Bifurcations of Planar Vector Fields, J.-P. Francoise and R. Roussarie (eds.), Lect. Notes in Math., N 1455, Springer, 1990, pp. 160-186 (with L. Gavrilov).  (цитирания -- 21)
  14. Limit cycles of perturbations of quadratic Hamiltonian vector fields, Jour. de Math. Pure et Appl., 72, 1993, pp.213-238 (with L. Gavrilov). (цитирания -- 26)
  15. On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems,  Jour. Diff. Eqns., 113,1,1994, pp.84-105 (with I.Iliev).   (цитирания -- 39)      PDF
  16. Hilbert-Arnold problem for cubic Hamiltonians. In: Proc. IV Int. Conf.    Diff. Eqns., D. Bainov (ed.), VSP Int. Publ., Utrecht, 1994     pp.115-124 (with I. Iliev). (цитирания -- 5)
  17. Toda orbits of Laguerre polynomials and representations of the Virasoro algebra,  Bull. Sci. Math, 117, 1993, pp.485-518 (with L. Haine).   (цитирания -- 31)                             
  18. On the isoenergetical non-degeneracy of the spherical pendulum, Phys. Lett. A, 173, 1993, pp.279-283.   (цитирания -- 14)
  19. On the number of the limit cycles in perturbations of quadratic Hamiltonian systems,  Proc. Lond. Math. Soc., 69, 1, 1994, pp.198-224  (with I.Iliev). PDF     (цитирания -- 109)
  20. Perturbations of quadratic Hamiltonian systems with symmetry, Annales IHP, Analyse non-lineaire,v.13,1,1996,pp.17-56 (with I.Iliev).  (цитирания -- 11)  http://www.numdam.org 
  21. Tau-functions as highest weight vectors for $W_{1+\infty$}-algebra,  Jour.Phys. A: Math. & Gen., 29, 1996, pp.5565-5573 (with B.Bakalov and M. Yakimov).  (цитирания -- 6) /hep-th/9510211
  22. Bispectral algebras of commuting ordinary differential operators, Comm. Math. Phys., 190, 1997, pp.331-373 (with B. Bakalov and M. Yakimov).  (цитирания -- 27)   /q-alg/9602011 
  23. Highest weight modules over $W_{1+\infty$-algebra and the bispectral problem,  Duke Math. J., 193, 1998, pp.41-72 (with B. Bakalov and M. Yakimov).  (цитирания -- 13)   /q-alg/9602012
  24. Backlund-Darboux transformations in Sato's Grassmannian, Serdica Math.J., 22, 4, 1996 pp.571-586 (with B. Bakalov and M. Yakimov).   (цитирания -- 20) /q-alg/9602010 
  25. General methods for constructing bispectral operators, Phys. Lett. A, 222, 1996, pp. 59-66 (with B.  Bakalov and M. Yakimov).  (цитирания -- 25) /q-alg/9605011 
  26. On the Krall-Hermitte and Krall-Bessel Polynomials, Int. Math. Res. Notices, 19, 1997, pp. 953-966 (with F. A. Gr\H{u}nbaum and L. Haine).   (цитирания -- 4)
  27. Highest weight modules of $W_{1+\infty}$, Darboux transformations and the bispectral problem, Proceedings of the Conference "Geometry and Mathematical Physics", Zlatograd 95, {\it Serdica Math. J.}, 23, 1997, pp. 95-112, (with B. Bakalov and M. Yakimov). (цитирания  -- 3)
  28. Automorphisms of the Weyl algebra and bispectral operators. In: The Bispectral Problem, Montreal, 1997, J. Harnad, A. Kasman (eds.), CRM Proc. Lecture Notes, 14, AMS, Providence, 1998, pp. 3-10 (with B. Bakalov and M. Yakimov).  (цитирания -- 3)  /q-alg/9707018
  29. The solution to the q-KdV equation,  Phys. Lett. A, 242, 3, 1998, pp. 139-151(with M. Adler and P. van Moerbeke). (цитирания -- 37)    PDF
  30. Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians,  Nonlinearity, 11, 6,1998,pp. 1521-1537 (with I. Iliev).  (цитирания -- 79)
  31. Some functions that generalize the Krall-Laguerre polynomials, Jour. Comp. Appl. Math., 106(2), 271-297, 1999 (with F.A.Grunbaum and L. Haine).   (цитирания -- 28)
  32. Darboux transformations for bispectral quantum integrable systems, Lett. Math. Phys. 49,(2), 131-143, 1999 (with A. Kasman). (цитирания -- 6)/math-ph/9806002  
  33. The Pfaff lattice and skew-orthogonal polynomials, Int. Math. Res. Notices, (11) 569-588, 1999 (with M. Adler and P. van Moerbeke). (цитирания -- 23)    PDF 
  34. Fuchsian bispectral operators, Bull. Sci. Math.,126, 2002 (with T.Milanov), pp.161-192. (цитирания -- 1)   PDF
  35. Bispectral operators of prime order,  Comm. Math. Phys.,231, pp.287-308, 2002.PDF
  36. Dual algebras of differential operators,  in: Kowalevski property, (Montreal), CRM Proc. Lecture Notes 32, Surveys from Kowalevski Workshop on Mathematical methods of Regular Dynamics, Leeds, April 2000 , Amer. Math. Soc., Providence (2002), pp. 121-148
  37. Strictly nilpotent elements and bispectral operators in the Wey algebra,  Bull. Sci. Math.,126, 2002, pp. 605-614.PDF, /math-ph/0206030
  38. The Weyl algebra, bispectral operators and dynamics of poles in integrable systems,  Reg. & Chaotic Dynamics, 2002, 7 (4), 399-424. (цитирания -- 1)
  39. Calogero-Moser spaces and an adelic W-algebra, Ann. de l'Inst. Fourier, v. 55, 2005, p. 2069-2090.  (цитирания -- 2)  PDF
  40. An adelic W-algebra and rank one bispectral operators, Bilinear Integrable Systems: From Classical to Quantum, From Continuous to Discrete. Proceedings of NATO Advanced Research Workshop, L. Fadeev, P. van Moerbeke, F. Lambert, edts., Springer, 2006. (цитирания -- 1)
  41. Non-integrability of some Painleve VI-equations and  dilogarithms, Regular & Chaotic Dynamics, v.12,  Issue 6, p.620-627, 2007.  (with Ts. Stoyanova),IF = 0.485. (цитирания -- 3)
  42. The trigonometric Grassmannian  and a difference $W$-algebra, Glasgow Math. J., Volume 51, pp 95-106  2009. (with L.Haine and P. I Iliev)
  43. The trigonometric Grassmannian  and a difference $W$-algebra, Transformation groups,vol. 15,1 , 2010, pp. 92-114 (with L.Haine and P. Iliev)   http://www.springerlink.com/content/u15q7259053q56x8/
     
  44. (with Mihajlova A)  An improved estimate for the number of zeros of Abelian integrals for cubic Hamiltonians  {\bf NONLINEARITY} Volume: 23 Issue: 12 Pp. 3053-3069    2010 .

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