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# Publications of Prof. Emil Horozov, Dr. Habil

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).
2. 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).
3. Uniqueness of limit cycles in planar vector fields which leave the axes invariant, Contemp. Math. 56, 1986, pp.117-129 (with St. van Gills).
4. On the non-integrability of Gross-Neveu models, Ann. Phys., 174, 1987, pp.430-441.

5. A Lax pair for the Kowalevski's top, Physica 29 D, 1987, pp.173-180 (with L.Haine).
6. The full geometry of the Kowalevski's top and (1-2)-Abelian varieties, Comm. Pure Appl. Math., v.42,4, pp.37-407 (with P.van Moerbeke).
7. Perturbations of the spherical pendulum and Abelian integrals,  Jour. reine angew. Math., 408, 1990, pp.114-135. PDF
8. 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).
9. Limit cycles of perturbations of quadratic Hamiltonian vector fields, Jour. de Math. Pure et Appl., 72, 1993, pp.213-238 (with L. Gavrilov).
10. 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).
11. Toda orbits of Laguerre polynomials and representations of the Virasoro algebra,  Bull. Sci. Math, 117, 1993, pp.485-518 (with L. Haine).
12. On the isoenergetical non-degeneracy of the spherical pendulum, Phys. Lett. A, 173, 1993, pp.279-283.
13. 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).
14. Perturbations of quadratic Hamiltonian systems with symmetry, Annales IHP, Analyse non-lineaire,v.13,1,1996,pp.17-56 (with I.Iliev). http://www.numdam.org
15. Tau-functions and modules over the Virasoro algebra. In: Abelian Varieties, W. Barth et al. (eds.), Berlin, New York, Walter de Gruyter,1995, pp.85-104 (with L. Haine).
16. 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). /hep-th/9510211
17. Bispectral algebras of commuting ordinary differential operators, Comm. Math. Phys., 190, 1997, pp.331-373 (with B. Bakalov and M. Yakimov). /q-alg/9602011
18. 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). /q-alg/9602012
19. Backlund-Darboux transformations in Sato's Grassmannian, Serdica Math.J., 22, 4, 1996 pp.571-586 (with B. Bakalov and M. Yakimov). /q-alg/9602010
20. General methods for constructing bispectral operators, Phys. Lett. A, 222, 1996, pp. 59-66 (with B.  Bakalov and M. Yakimov). /q-alg/9605011
21. 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).
22. 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). /q-alg/9707018
23. The solution to the q-KdV equation,  Phys. Lett. A, 242, 3, 1998, pp. 139-151(with M. Adler and P. van Moerbeke).  PDF
24. Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians,  Nonlinearity, 11, 6,1998,pp. 1521-1537 (with I. Iliev).
25. Some functions that generalize the Krall-Laguerre polynomials, Jour. Comp. Appl. Math., 106(2), 271-297, 1999 (with F.A.Grunbaum and L. Haine).
26. Darboux transformations for bispectral quantum integrable systems, Lett. Math. Phys. 49,(2), 131-143, 1999 (with A. Kasman). /math-ph/9806002
27. The Pfaff lattice and skew-orthogonal polynomials, Int. Math. Res. Notices, (11) 569-588, 1999 (with M. Adler and P. van Moerbeke). PDF
28. Fuchsian bispectral operators, Bull. Sci. Math.,126, 2002 (with T.Milanov), pp.161-192.PDF
29. Bispectral operators of prime order,  Comm. Math. Phys.,231, pp.287-308, 2002.PDF
30. 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.
31. Strictly nilpotent elements and bispectral operators in the Wey algebra,  Bull. Sci. Math.,126, 2002, pp. 605-614.PDF, /math-ph/0206030
32. The Weyl algebra, bispectral operators and dynamics of poles in integrable systems,  Reg. & Chaotic Dynamics, 2002, 7 (4), 399-424.
33. Calogero-Moser spaces and an adelic W-algebra, Ann. de l'Inst. Fourier, v. 55, 2005, p. 2069-2090. PDF