Alexandre M. Vinogradov

Alexandre M. VINOGRADOV

Full professor in mathematics,
Salerno University (Italy).

Office address: Dipartimento di Matematica ed Informatica, Facolta' di Scienze Matematiche, Fisiche e Naturali, Universita' degli Studi di Salerno, Via Ponte del Melillo, 84084 Fisciano (SA) Italy

E-mail: vinograd @ unisa.it
Tel. No. +39-089.963.328
Fax No. +089-963303
Secretary's No. +089-963300
Date of birth: February 18, 1938
Education: Moscow Mekh-mat (Mechanical & Mathematical Faculty of Moscow State Univ.), 1960
Degrees: Ph.D. (Cand. Sc. Phys.-Math.) in Math.,
Moscow State University, 1964.
Doctor of Science in Math., Mathematics Institute of Siberian
Branch of USSR Academy of Science, Novosibirsk, 1984

Publications in Diffeotopy

Newest and forthcoming

Past years:
1999-1994, 1994-1990, 1989-1986, 1985-1984, 1983-1979, 1978-1972

2004

D. Catalano Ferraioli and A. M. Vinogradov - Ricci flat 4-metrics with bidimensional null Killing orbits, DIPS 07/2004.
Ricardo J. Alonso-Blanco and A. M. Vinogradov - Green Formula and Legendre Transformation, Acta Appl. Math., Vol. 83, No. 1-2, (2004), pp. 149-166. See also DIPS 5/2003.
Jorge Cortés and Alexandre M. Vinogradov - Hamiltonian theory of constrained impulsive motion, DIPS-2/2004.
2003
G. Vezzosi, A. Vinogradov - On higher order analogues of De Rham cohomology, - Diff. Geom. and Appl. 19 (2003), 29-59.
2002
Smooth manifolds and observables - Springer-Verlag, Graduate Texts in Mathematics, Vol. 220, 2002, XIII+222 pp., ISSBN 0-387-95543-7. In collaboration with A. M. Astashev, A. V. Bocharov, S. V. Duzhin, A. B. Sossinsky, M. M. Vinogradov.
A. Vinogradov and M. Vinogradov - Graded multiple analogs of Lie algebras, - Acta Appl. Math., Volume 72, Issue 1-2, pp. 183-197, June 2002. See also DIPS 8/2001.
F. Pugliese, A. M. Vinogradov - Geometry of inelastic collisions, - Acta Appl. Math., Volume 72, Issue 1-2, pp. 77-85, June 2002. See also DIPS 1/2001.
G. Sparano, G. Vilasi, A. M. Vinogradov - Vacuum Einstein metrics with bidimensional Killing leaves. II. Global aspects, - J. Diff. Geom. and Appl., Volume 17, Issue 1, July 2002, pp. 15-35. See also DIPS 14/2001.
G. Sparano, G. Vilasi, A. M. Vinogradov - Vacuum Einstein metrics with bidimensional Killing leaves. I. Local aspects, - J. Diff. Geom. and Appl., Volume 17 Issue 2, March 2002, pp. 95-120. See also DIPS 13/2001.
2001
A. M. Vinogradov - Cohomological Analysis of Partial Differential Equations and Secondary Calculus, - AMS "Translation of Mathematical Monographs" series, vol. 204, 247 pages, 2001.
G. Sparano, G. Vilasi, A. M. Vinogradov - Gravitational fields with a non abelian bidimensional Lie algebra of symmetries, - Phys. Lett., B 513, No.1-2, 142-146 (2001). See also the Diffiety Inst. Preprint Series, DIPS 12/2001.
F.Pugliese, A. M. Vinogradov - Discontinuous trajectories of Lagrangian systems with singular hypersurface, - J. Math. Phys. 42(1), 2001, pp. 309-329.
2000
Smooth manifolds and observables, - textbook, MCCME, Moscow, 2000, 300 pp., ISSBN 5-900916-57-X (in Russian). In collaboration with A. M. Astashev, A. V. Bocharov, S. V. Duzhin, A. B. Sossinsky, M. M. Vinogradov.
F. Pugliese, A. M. Vinogradov - On the geometry of singular lagrangians, - J. Geom. and Phys., 35 (1), 2000, pp. 35-55. See also the Diffiety Inst. Preprint Series, DIPS 2/99.
1999
V. N. Chetverikov, A. B. Bocharov, S. V. Duzhin, N. G. Khor'kova, I. S. Krasil'shchik, A. V. Samokhin, Y. N. Torkhov, A. M. Verbovetsky, A. M. Vinogradov - Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, - I. S. Krasil'shchik, and A. M. Vinogradov, Editors - AMS, 1999, approximately 347 pp., MMONO/182.
1998
F. Pugliese, A. M. Vinogradov - Jumping oscillator, - The Diffiety Inst. Preprint Series, DIPS 11/98.
A. Vinogradov - Introduction to secondary calculus, - in M. Henneaux, I. Krasil'shchik, and A. Vinogradov (Eds.), Secondary Calculus and Cohomological Physics, Contemporary Mathematics, vol. 219, American Mathematical Society, 1998. See also The Diffiety Inst. Preprint Series, DIPS 5/98.
A. Vinogradov and M. Vinogradov - On multiple generalizations of Lie algebras and Poisson manifolds, - in M. Henneaux, I. Krasil'shchik, and A. Vinogradov (Eds.), Secondary Calculus and Cohomological Physics, Contemporary Mathematics, vol. 219, American Mathematical Society, 1998. See also The Diffiety Inst. Preprint Series, DIPS 6/98.
G. Vezzosi, A. Vinogradov - On higher de Rham cohomology, - Preprint di Matematica - n.19, Scuola Normale di Pisa (1998), 37 pp.
G. Marmo, G. Vilasi, A. M. Vinogradov - The local structure of n-Poisson and n-Jacobi manifolds, - Journal of Geometry and Physics, 25 (1998), pp. 141 - 182. (The full text (PDF 244883 bytes) can be found on the journal home page.) See also The Diffiety Inst. Preprint Series, DIPS 3/97.

1997

Algebraic Aspects of Differential Calculus (a collection of papers, edited by A. M. Vinogradov and I. S. Krasil'shchik). A special issue of Acta Applicandae Mathematicae, Volume 49, Issue 3, December 1997. See also The Diffiety Inst. Preprint Series , DIPS 1/96 - DIPS 8/96
Vezzosi G., Vinogradov A. M. - Infinitesimal Stokes' formula for higher order de Rham complexes, - Acta Applicandae Mathematicae, Volume 49, Issue 3, December 1997, pp. 311-329.
Symmetries of Differential Equations in Mathematical Physics and Natural Sciences (a monograph by V. N. Chetverikov, A. B. Bocharov, S. V. Duzhin, N. G. Khor'kova, I. S. Krasil'shchik, A. V. Samokhin, Y. N. Torkhov, A. M. Verbovetsky, A. M. Vinogradov, edited by A. M. Vinogradov and I. S. Krasil'shchik). Factorial Publ. House, 1997 (in Russian).

1996

Michor P. W., Vinogradov A. M., n-ary Lie and associative algebras, - Rendiconti del Seminario Matematico, Universita'e politecnico Torino, Vol. 53, 4 (1996), pp. 373-392. Also see Preprint of the Erwin Schroedinger International Inst. for Mathematical Physics (1996), no. 402, Wien, 18 pp. TeX-file see on the ESI WWW-server
1994
Lizzi F., Marmo G., Sparano G., Vinogradov A. M. - Eikonal type equations for geometrical singularities of solutions in field theory, - J. Geom. and Phys., 14 (1994)
Modugno M., Vinogradov A. M. - Some variations on the notion of connection, - Annali di Matematica pyra ed applicata, 167 (1994), 33-71.
Vinogradov A. M. - From symmetries of partial differential equations towards secondary ("quantized") calculus, - J. Geom. and Phys., 14 (1994), 146-194.
1992
Cabras A., Vinogradov A. M. - Extension of the Poisson bracket to differential forms and multi-vector fields, - J. Geom. and Phys., 9 (1992) 1, 75-100.
Verbovetsky A. M., Vinogradov A. M., Gessler, D. M. - Scalar differential invariants and characteristic classes of homogeneous geometric structures, - (Russian) Mat. Zametki, 51 (1992), no. 6, 15-26. English translation in Math. Notes, 51 (1992), no. 5-6, 543-549.
1991
Vinogradov A. M. Scalar differential invariants, diffieties, and characteristic classes, - in: Francaviglia M. (Ed.), Mechanics, Analysis and Geometry: 200 Years after Lagrange, (1991), Elsvier, Amsterdam, 379-416.
Alekseevski D. V., Lychagin V. V., Vinogradov A. M. - Basic ideas and concepts of differential geometry, - Encyclopedia of Math. Sciences, 28 (1991), Springer-Verlag, Berlin.
Modugno M., Vinogradov A. M. - Some variations on the notion of connection, - (1991) 13, Dip. Mat. Appl. "G. Sansone", Univ. Stud. Firenze, Firenze.
1990
Vinogradov A. M., Yumaguzhin V. A. - Differential invariants of webs on two-dimensional manifolds , - (Russian) Mat. Zametki, 48 No 1, (1990), 26-37. English translation in Math. Notes, 48 (1990), no. 1-2, 639-647 (1991).
Vinogradov A. M. - The union of the Schouten and Nijenhuis brackets, cohomology, and superdifferential operators, - (Russian) Mat. Zametki, 47 (1990), no. 6, 138-140. English translation in Math. Notes.
1989
Vinogradov A. M. - Symmetries and conservation laws of partial differential equations: basic notions and results. - Symmetries of partial differential equations. Part I, Acta Appl. Math., 15 (1989), no. 1-2, 3-21.
Vinogradov A. M. (ed.) - Symmetries of partial differential equations, Conservation laws - applications - algorithms, - Reprint of Acta Appl. Math. 15 (1989), no. 1-2, and 16 (1989), no. 1 and no. 2. Kluwer Academic Publishers, Dordrecht, 1989. vi+456 pp.
Krasil'shchik I. S., Vinogradov A. M. - Nonlocal trends in the geometry of differential equations: symmetries, conservation laws, and Baecklund transformations, - Acta Appl. Math., 15 (1989) 1-2, 161-209. Also in: Vinogradov A. M. (Ed.), Symmetries of Partial Differential Equations, (1989), Kluwer Academic Publishers, Dordrecht, Boston, London, 161-209.
Gusyatnikova V. N., Samokhin A. V., Titov V. S., Vinogradov A. M., Yumaguzhin, V. A. - Symmetries and conservation laws of Kadomtsev-Pogutse equations (their computation and first applications). - Symmetries of partial differential equations. Part I., Acta Appl. Math. 15 (1989), no. 1-2, 23-64. Also in: Vinogradov A. M. (Ed.), Symmetries of Partial Differential Equations, (1989), Kluwer Acad. Publ., Dordrecht, Boston, London, 23-64.
1988
Vinogradov A. M. - An informal introduction to the geometry of jet spaces, - Conference on Differential Geometry and Topology (Sardinia, 1988). Rend. Sem. Fac. Sci. Univ. Cagliari 58 (1988), suppl., 301-333.
Senashov S. I., Vinogradov A. M. - Symmetries and conservation laws of 2-dimensional ideal plasticity, - Proc. Edinburgh Math. Soc., 31 (1988), 415-439.
Alekseevski D. V., Lychagin V. V., Vinogradov A. M. - Basic ideas and concepts of differential geometry, - Modern problems of mathematics: fundamental directions, Vol. 28, (1988), 298 p., Akad. Nauk SSSR, VINITI, Moscow (Russian).
1987
Vinogradov A. M. - Integrability and symmetries, - in Nonlinear waves. Structures and bifurcations, Moscow, Nauka, 1987, pp. 279-290 (Russian).
1986
Astashov A. M., Vinogradov A. M. - On the structure of Hamiltonian operator in field theory, - J. Geom. and Phys., 3 (1986), no. 2, 263-287.
Vinogradov A. M. - Geometric singularities of solutions of nonlinear partial differential equations, - Differential geometry and its applications (Brno, 1986), 359-379, Math. Appl. (East European Ser.), 27, Reidel, Dordrecht-Boston, MA, 1987.
Krasil'shchik I. S., Lychagin V. V., Vinogradov A. M. - Geometry of Jet Spaces and Nonlinear Differential Equations, - Advanced Studies in Contemporary Mathematics, 1 (1986), Gordon and Breach, New York, London. xx+441 pp.
Vinogradov A. M., Krasil'shchik I. S., Lychagin, V. V. - Introduction to the geometry of nonlinear differential equations, - (Russian) Nauka, Moscow, 1986. 336 pp.
Vinogradov A. M., Samokhin A. V. - Cartan-Kaehler theorem, - (Russian) Transactions of the Seminar of Algebra and Geometry of Differential Equations, VINITI, n. 858-B, Moscow, 1986, pp. 112-132.
Vinogradov A. M., Samokhin A. V. - On factorization of equations, - (Russian) Transactions of the Seminar of Algebra and Geometry of Differential Equations, VINITI, n. 858-B, Moscow, 1986, pp. 133-146.
Vinogradov A. M. - Geometry of differential equations, secondary differential calculus and quantum field theory, - (Russian) Izv. Vyssh. Uchebn. Zaved. Mat., 1986, no. 1, 13-21.
1985
Gusyatnikova V. N., Vinogradov A. M., Yumaguzhin V. A. - Secondary differential operators, - J. Geom. and Phys., v. 2, No 2, (1985), 23-65.
Vinogradov A. M., Gusyatnikova V. N., Yumaguzhin V. A. - Secondary differential operators, - Dokl. Akad. Nauk SSSR 283 (1985), no. 4, 801-805 (Russian). English translation in Soviet Math. Dokl., vol. 32 (1985), No. 1.
1984
Vinogradov A. M. - Category of partial differential equations, - Lecture Notes in Math., 1108 (1984), Springer-Verlag, Berlin, 77-102.
Vinogradov A. M. - The C-spectral sequence, Lagrangian formalism, and conservation laws. I. The linear theory., - J. Math. Anal. Appl. 100 (1984), no. 1, 1-40.
Vinogradov A. M. - The C-spectral sequence, Lagrangian formalism, and conservation laws. II. The nonlinear theory., - J. Math. Anal. Appl. 100 (1984), no. 1, 41-129.
Vinogradov A. M. - Local symmetries and conservation laws, - Acta Appl. Math., 3 (1984), 21-78.
Krasil'shchik I. S., Vinogradov A. M. - Nonlocal symmetries and the theory of coverings, - an addendum to A. M. Vinogradov's Local symmetries and conservation laws, Acta Appl. Math., v. 2, No 1, (1984), 79-96.
Vinogradov A. M., Krasil'shchik I. S. - On the theory of nonlocal symmetries of nonlinear partial differential equations, - Dokl. Akad. Nauk SSSR 275 (1984), no. 5, 1044-1049 (Russian); Soviet Math. Dokl., 29 (1984), No 2, pp. 337 - 341 (English).
Vinogradov A. M. - The category of differential equations and its significance for physics, - in: Krupka D. (Ed.), Proc. Conf. Diff. Geom. Appl. (Brno, 1984), (1984), J.E. Purkyne Univ., Brno, Czechoslovakia, 289-301.
Vinogradov A. M. - Higher symmetries and conservation laws of general systems of nonlinear partial differential equations, - (Russian) Uspehi Mat. Nauk 39, No 1 (1984), 182-183.
1983
Vinogradov A. M. - Category of nonlinear differential equations, - (Russian) addendum to: Pommaret J.-F., Systems of partial differential equations and Lie pseudogroups. Translated from the English by A. V. Bocharov, M. M. Vinogradov and I. S. Krasil'shchik. Translation edited and with a preface by A. M. Vinogradov. ``Mir'', Moscow, 1983. 400 pp.
Vinogradov A. M. - Higher symmetries and conservation laws, - in Group-theoretic methods in physics, vol. 2, Moscow, Nauka, 1983, pp. 414-420.
1982
Vinogradov A. M. - Category of nonlinear differential equations, - (Russian) Equations on manifolds, Novoe Global. Anal., Voronezh. Gos. Univ., Voronezh, 1982, 26-51.
Krasil'shchik I. S., Lychagin, V. V., Vinogradov A. M. - Geometry of nonlinear differential equations, - Moscow Institute of Electronic Engineering, Moscow, 1982 (in Russian).
Vinogradov A. M. - Conservation laws, Spencer cohomology and the C-spectral sequence, - in "Leningrad international topologic conference", Leningrad, Nauka, 1982, p. 166.
1981
Vinogradov A. M. - Geometry of nonlinear differential equations, - J. Sov. Math., 17 (1981), 1624-1649.
Vinogradov A. M., Krasil'shchik I. S. - What is the Hamiltonian formalism? - London Math. Soc. Lect. Notes Ser., 60 (1981), Cambridge Univ. Press, London, 241-266.
Vinogradov A. M., Kupershmidt B.A. - The structure of Hamiltonian mechanics, - London Math. Soc. Lect. Notes Ser., 60 (1981), Cambridge Univ. Press, London, 173-239.
Vinogradov A. M. - Category of nonlinear differential equations, - (Russian) in "XV Voronezh winter mathematical school", Voronezh, Voronezh Gos. Univ. Publ., VINITI, No 5691, 1981, 9-10.
1980
Vinogradov A. M., Krasil'shchik I. S. - A method of computing higher symmetries of nonlinear evolution equations and nonlocal symmetries, - Soviet Math. Dokl., 22 (1980), 235-239.
Vinogradov A. M. - The geometry of nonlinear differential equations, - Problems in geometry, Vol. 11 (Russian), pp. 89-134, Akad. Nauk SSSR, VINITI, Moscow, 1980 (in Russian).
1979
Vinogradov A. M. - Some homological systems associated with differential calculus over commutative algebras, - Russian Math. Surveys, 34 (1979) 6, 250-255.
Vinogradov A. M. - The theory of higher infinitesimal symmetries of nonlinear partial differential equations, - Soviet Math. Dokl., 20 (1979), 985-990.
1978
Vinogradov A. M. - A spectral system associated with a non-linear differential equation, and the algebro-geometric foundations of Lagrangian field theory with constraints, - Soviet Math. Dokl., 19 (1978), 144-148.
Vinogradov A. M. - Hamiltonian structures in field theory, - Soviet Math. Dokl., 19 (1978), 790-794.
1977
Vinogradov A. M. - On the algebro-geometric foundations of Lagrangian field theory, - Soviet Math. Dokl., 18 (1977), 1200-1204.
Vinogradov A. M., Kupershmidt B.A. - The structure of Hamiltonian mechanics, - Russian Math. Surveys, 32, No 4, (1977), 175-236.
Vinogradov A. M., Krasil'shchik I. S., Lychagin V. V. - Application of nonlinear differential equations in civil aviation, - (Russian) Moskov. Inst. Inz. Grazdan. Aviacii, Moscow, 1977. 123 pp.
Vinogradov A. M. - The geometry of jet spaces, - Uspekhi mat. nauk, 32, No 4, (1977).
1976
Vinogradov A. M., Vorobjev E.M. - Applications of symmetries to finding exact solutions of Zabolotskaya-Khokhlov equation, - (Russian) Akust. Zh., 22, (1976), 23-27.
1975
Vinogradov A. M., Krasil'shchik I. S. - What is the Hamiltonian formalism? - Russian Math. Surveys, 30 (1975), 177-202 (Russian).
1974
Vinogradov A. M. - The theory of symmetries of nonlinear partial differential equations, - Moscow, VINITI, No 2855-74 (1974), 16 pp.
1973
Vinogradov A. M. - Multivalued solutions and a classification principle for differential equation, - Soviet Math. Dokl., 14 (1973), 661-665.
1972
Vinogradov A. M. - The logic algebra for the theory of linear differential operators, - Soviet Math. Dokl., 13 (1972), 1058-1062.