Инварианты голоморфных многомерных дискретных динамических систем
Автор(ы):
Валентин Юрьевич Тыщенко
Гродненский государственный университет,
факультет математики и информатики
valentinet@mail.ru
Аннотация:
Рассматриваются функциональные инварианты голоморфных многомерных дискретных динамических систем
а также некоторые нелокальные топологические характеристики связанных с системами инвариантных слоений
Ссылки:
- Cayley A. Memoire sur les Hyperdeterminants // Journ. reine angew. Math. - 1846. - V. 30. - P. 1 - 37
- Hilbert D. Gesammelte Abhandlungen. Bd. 2. Algebra, Invariantentheorie, Geometrie. Zweite Auflage. - Berlin - Heidelberg - New York: Springer, 1970. - 453 с
- Laguerre E. Sur les equations lineaires du troisieme ordre // C. r. Acad. sci. - 1879. - V. 88. - P. 116 - 119
- Halphen G. H. Syr la reduction des equations differentielles lineaires aux formes integrables // mem. pres. par divers savants a l` Acad. des Sci. - 1884. - V. 28. - P. 1 - 260
- Liouville R. Sur certaines equations dfferentielles du premier ordre // C. r. Acad. sci. - 1886. - V. 103. - P. 476 - 479
- Appel P. Sur les invariants de quelques equations differentielles // Journ. Math. pures et appl. - 1889. - V. 5. - P. 361 - 423
- Painleve P. Sur une transformation des equations differentielles du premier ordre // C. r. Acad. sci. - 18906. - V. 110. - P. 840 - 843
- Sibirskii К. S. Algebraic invariants of differential equations. - Kishinev. : Shtiinca, 1982. - 269 p
- Sibirskii К. S. Introduction in the algebraic theory of invariants of differential equations and matrixes. - Kishinev. : Shtiinca, 1976. - 169 p. (In Russian)
- Belitskii G. R. Normal forms, invariants and local maps. - Kiev. : Naukova dumka, 1979. - 254 p. (In Russian)
- Gorbuzov V. N., Tyshchenko V. Yu. On the classification of the covering coliations // Differential Equations and Control Processes (http://http://www. math. spbu. ru/diffjournal). - 2004. N. 4. - P. 1 - 19. (In Russian)
- Gorbuzov V. N. Integrals of differential systems. - Grodno: GrGU, 2006. - 447 p. (In Russian)
- Gayshun I. V. Completely solvable many-dimensional differential equations. - Minsk: Nauka i tekhnika, 1983. - 272 p. (In Russian)
- Dubrovin B. A., Novikov S. P., Fomenko A. T. Modern geometry: Methods and applications. - Moscow: Nauka, 1986. - 760 p. (In Russian)
- Nemytskii V. V. To the theory of orbits of the general dynamical systems // Matematicheskii sbornik. - V. 23, issue 2. - P. 161 - 186. (In Russian)
- Tyshchenko V. Yu. On invariants of discrete dynamical systems // Differentsial, nye Uravneniya. - 2010. - V. 46, N. 5. - P. 752 - 755. (In Russian)
- Belitskii G. R., Tkachenko V. A. Analytic solvability of many-dimensional functioanal equation in a neighborhood of a nonsingular point // Teoriya funktsii, funktsional'nyi analiz i ikh prilozheniya, Kharkov. - Issue 58. - 1992. - P. 7 - 21. (In Russian)
- Tyshchenko V. Yu. Basis of absolute invariants of completely solvable linear and linear-fractional discrete dynamical systems // Differentsial, nye Uravneniya. - 2012. - V. 48, N. 5. - P. 758 - 760. (In Russian)
- Gantmakher F. R. Theory of matrixs. - Moscow: Nauka, 1988. - 550 p. (In Russian)
- Tyshchenko V. Yu. On the classifications of foliations, defined by complex linear and linear-fractional discrete dynamical systems // Vestnik BGU. Ser. 1. - 2012. - N. 3. - P. 125 - 130. (In Russian)
- Gorbuzov V. N., Tyshchenko V. Yu. R-holomorphic solutions of total differential equation // Differentsial, nye Uravneniya. - 1999. - V. 35, N. 4. - P. 447 - 452. (In Russian)
- Gorbuzov V. N., Tyshchenko V. Yu. On R-holomorphic solutions of system of total differential equations // Vesci NAN Belarusi. Ser. fiz. -мат. navuk. - 1999. - N. 3. - P. 124 - 126. (In Russian)
- Tyshchenko V. Yu. Covering foliations of differential systems. - Grodno: GrGU, 2011. - 180 p. (In Russian)
- Ladis N. N. On integral curves of complex homogeneous equation // Differentsial, nye Uravneniya. - 1979. - V. 15, N. 2. - P. 246 - 251. (In Russian)
- Gorbuzov V. N., Tyshchenko V. Yu. On the equivalence of foliations of linear differential systems // Differentsial, nye Uravneniya. - 2003. - V. 39, N. 12. - P. 1596 - 1599. (In Russian)
- Guckenheimer J. Hartman's theorem for complex flows in the Poincare domain // Compos. math. - 1972. - V. 24, N. 1. - P. 75 - 82
- Ladis N. N. Topological invariants of complex liner flows // Differentsial, nye Uravneniya. - 1976. - V. 12, N. 12. - P. 2159 - 2169. (In Russian)
- Ladis N. N. Topological equivalence of hyperbolic linear systems // Differentsial, nye Uravneniya. - 1977. - V. 13, N. 2. - P. 255 - 265. (In Russian)
- Il'yashenko Yu. S. Remarks on the topology of singular points of analytic differential equations in the complex domain and Ladis theorem // Funktsional'nyi analiz i ego prilozheniya. - 1977. - V. 11, N. 2. - P. 28 - 38. (In Russian)
- Camacho C., Kuiper N. H., Palis J. The topology of holomorphic flows with singularity. 1 // Publications mathematiques de l`I. H. E. S, Paris. - 1978. - V. 48. - P. 5 - 38
- Gorbuzov V. N., Tyshchenko V. Yu. Particular integrals of systems of ordinary differential equations // Matematicheskii sbornik. - 1992. - V. 183, N. 3. - P. 76 - 94. (In Russian)
- Tyshchenko V. Yu. On compact invariant hypersurfaces of discrete dynamical systems // Differentsial, nye Uravneniya. - 2008. - Т. 44, N. 7. - P. 1005 - 1006. (In Russian)
- Goursat E. Calculus course. V. 2, P. 2. - Moscow, Leningrad: GTTI, 1933. - 287 p. (In Russian)