Geodesic
On the transcendental functions connected with integration of differential equations in finite terms
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIV, Tome 432 (2015), pp. 196-223 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

@article{ZNSL_2015_432_a11,
     author = {M. D. Malykh},
     title = {On the transcendental functions connected with integration of differential equations in finite terms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {196--223},
     year = {2015},
     volume = {432},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_432_a11/}
}
TY  - JOUR
AU  - M. D. Malykh
TI  - On the transcendental functions connected with integration of differential equations in finite terms
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2015
SP  - 196
EP  - 223
VL  - 432
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2015_432_a11/
LA  - ru
ID  - ZNSL_2015_432_a11
ER  - 
%0 Journal Article
%A M. D. Malykh
%T On the transcendental functions connected with integration of differential equations in finite terms
%J Zapiski Nauchnykh Seminarov POMI
%D 2015
%P 196-223
%V 432
%U http://geodesic.mathdoc.fr/item/ZNSL_2015_432_a11/
%G ru
%F ZNSL_2015_432_a11
M. D. Malykh. On the transcendental functions connected with integration of differential equations in finite terms. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIV, Tome 432 (2015), pp. 196-223. http://geodesic.mathdoc.fr/item/ZNSL_2015_432_a11/

[1] J. M. Borwein, R. E. Crandall, “Closed forms: what they are and why we care”, Notices Amer. Math. Soc., 60:1 (2013), 50–65 | DOI | MR | Zbl

[2] M. F. Singer, “Liouvillian first integral of differential equations”, Trans. Amer. Math. Soc., 333:2 (1992), 673–688 | DOI | MR | Zbl

[3] G. Casale, “Liouvillian first integrals of differential equations”, Banach Center Publ., 94 (2011), 153–161 | DOI | MR | Zbl

[4] J. Moses, Symbolic integration, AI Technical Reports, 1967 | MR

[5] E. S. Cheb-Terrab, L. G. S. Duarte, L. A. C. P. da Mota, “Computer algebra solving of first order ODEs using symmetry methods”, Comput. Phys. Commun., 101 (1997), 254–268 | DOI | MR | Zbl

[6] E. S. Cheb-Terrab, A. D. Roche, “Symmetries and first order ODE patterns”, Comput. Phys. Commun., 113 (1998), 239–260 | DOI | MR | Zbl

[7] E. S. Cheb-Terrab, A. D. Roche, “Integrating factors for second order ODEs”, J. Symb. Comput., 27:5 (1999), 501–519 | DOI | MR | Zbl

[8] E. S. Cheb-Terrab, T. Kolokolnikov, “First order ODEs, symmetries and linear transformations”, Europ. J. Appl. Math., 14:2 (2003), 231–246 | DOI | MR | Zbl

[9] D. D. Mordukhai-Boltovskoi, “Kommentarii k Evklidu”, Nachala Evklida, Knigi 1–6, GTTI, M., 1955

[10] N. A. Kudryashov, Analiticheskaya teoriya nelineinykh differentsialnykh uravnenii., Institut kompyuternykh issledovanii, Izhevsk, 2004

[11] A. R. Its, A. A. Kapaev, V. Yu. Novokshenov, A. S. Fokas, Transtsendenty Penleve. Metod zadachi Rimana, Ratsionalnaya i khaoticheskaya dinamika, M.–Izhevsk, 2005

[12] C. L. Sobolevskii, Podvizhnye osobye tochki reshenii obyknovennykh differentsialnykh uravnenii, BGU, Minsk, 2006

[13] V. V. Golubev, Lektsii po analiticheskoi teorii differentsialnykh uravnenii, GITTL, M.–L., 1950

[14] L. Schlesinger, Einfuhrung in die Theorie der gewohnlichen Differentialgleichungen, VWV, Leipzig, 1922

[15] N. N. Parfentev, “Otzyv o rabote prof. Shlezingera iz Gissena”, Izvestiya fiz.-mat. obschestva pri imp. Kazanskom universitete, 2-ya ser., 43:4 (1912)

[16] P. Painlevé, “Leçons sur la théorie analytique des équations différentielles”, Paris, 1897, ØE uvres, v. 1, Paris, 1973

[17] P. Painlevé, “Mémoire sur les équations différentielles du premier ordre”, ØE uvres, v. 2, Paris, 1974, 237–461

[18] P. Painlevé, “Prilozhenie k knige P. Boutroux”, ØE uvres, V. 2, Paris, 1974, 767–813

[19] A. N. Bogolyubov, M. D. Malykh, “Transtsendentnye funktsii, vvodimye integrirovaniem differentsialnykh uravnenii”, Dinamika slozhnykh sistem – XXI vek, Vyp. 3, 2010

[20] L. Koenigsberger, Lehrbuch der Theorie der Differentialgleichungen mit einer unabhägigen Variabeln, Tuebner, Leipzig, 1889

[21] L. Koenigsberger, Die Principien der Mechanik, Tuebner, Leipzig, 1901

[22] A. M. Vinogradov, I. S. Krasilschik (red.), Simmetrii i zakony sokhraneniya uravnenii matematicheskoi fiziki, Faktorial, M., 1997

[23] R. Khartskhorn, Algebraicheskaya geometriya, Mir, M., 1981 | MR

[24] O. Zarisskii, P. Samyuel, Kommutativnaya algebra, IL, M., 1963

[25] D. Maclagan, B. Sturmfels, Introduction to Tropical Geometry, http://homepages.warwick.ac.uk/staff/D.Maclagan/papers/TropicalBook.html

[26] K. Zigel, Lektsii po nebesnoi mekhanike, IL, M., 1959

[27] J. Liouville, “Memoire sur l'integration d'une classe de fonctions transcendantes”, J. Reine Angew. Math., 13 (1835), 93–118 | DOI | Zbl

[28] J. F. Ritt, Integration in Finite Terms: Liouville's Theory of Elementary Methods, Columbia Univ. Press, New York, 1949 | MR

[29] A. G. Khovanskii, Topologicheskaya teoriya Galua. Razreshimost i nerazreshimost uravnenii v konechnom vide, Izd-vo MTsNMO, M., 2008

[30] M. Bronstein, Symbolic Integration I: Transcendental Functions, Springer, Berlin, 1999 | MR

[31] N. G. Chebotarev, Teoriya algebraicheskikh funktsii, URSS, M., 2013

[32] G. Castelnuovo, F. Enriques, “Die algebraischen Flachen vom Gesichtspunkte der birationalen Transformationen aus”, Enzyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, III, 2, Teil C: Algebraische Geometrie, Teubner, Leipzig, 1915, 674–768

[33] F. Enriques, Le superficie algebriche, Bologna, 1946

[34] Yu. G. Prokhorov, Gruppa Kremony i ee podgruppy, Zasedaniya Moskovskogo matematicheskogo obschestva, 26 marta 2013 g.