Geodesic
I. G. Petrovskii, Hilbert's topological problems, and modern mathematics
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 57 (2002) no. 4, pp. 833-845 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{RM_2002_57_4_a19,
     author = {V. I. Arnol'd},
     title = {I. {G.~Petrovskii,} {Hilbert's} topological problems, and modern mathematics},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {833--845},
     year = {2002},
     volume = {57},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2002_57_4_a19/}
}
TY  - JOUR
AU  - V. I. Arnol'd
TI  - I. G. Petrovskii, Hilbert's topological problems, and modern mathematics
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2002
SP  - 833
EP  - 845
VL  - 57
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/RM_2002_57_4_a19/
LA  - en
ID  - RM_2002_57_4_a19
ER  - 
%0 Journal Article
%A V. I. Arnol'd
%T I. G. Petrovskii, Hilbert's topological problems, and modern mathematics
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2002
%P 833-845
%V 57
%N 4
%U http://geodesic.mathdoc.fr/item/RM_2002_57_4_a19/
%G en
%F RM_2002_57_4_a19
V. I. Arnol'd. I. G. Petrovskii, Hilbert's topological problems, and modern mathematics. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 57 (2002) no. 4, pp. 833-845. http://geodesic.mathdoc.fr/item/RM_2002_57_4_a19/

[1] O. Ya. Viro, “O topologii veschestvennykh algebraicheskikh mnogoobrazii”, UMN, 41:3 (1986), 47–67 | MR

[2] V. M. Kharlamov, “Topologiya deistvitelnykh algebraicheskikh mnogoobrazii”, I. G. Petrovskii. Sistemy uravnenii s chastnymi proizvodnymi. Algebraicheskaya geometriya: Izbr. trudy, Nauka, M., 1986, 465–493 | MR

[3] D. A. Gudkov, “Topologiya veschestvennykh proektivnykh algebraicheskikh mnogoobrazii”, UMN, 29:4 (1974), 3–79 | MR | Zbl

[4] V. I. Arnold, “O raspolozhenii ovalov veschestvennykh ploskikh algebraicheskikh krivykh, involyutsiyakh chetyrekhmernykh gladkikh mnogoobrazii i arifmetike tselochislennykh kvadratichnykh form”, Funkts. analiz i ego pril., 5:3 (1971), 1–9 | MR | Zbl

[5] V. A. Rokhlin, “Sravneniya po modulyu 16 v shestnadtsatoi probleme Gilberta. II”, Funkts. analiz i ego pril., 7:2 (1973), 91–92 | Zbl

[6] I. G. Petrovsky, “Sur la topologie des courbes réelles et algébriques”, C. R. Acad. Sci. Paris, 197 (1933), 1270–1273

[7] I. G. Petrowsky, “On the topology of real plane algebraic curves”, Ann. of Math. (2), 39 (1938), 189–209 | DOI | MR | Zbl

[8] I. G. Petrovskii, O. A. Oleinik, “O topologii deistvitelnykh algebraicheskikh poverkhnostei”, Izv. AN SSSR. Ser. matem., 13 (1949), 389–402 | MR | Zbl

[9] O. A. Oleinik, “Otsenki chisel Betti deistvitelnykh algebraicheskikh giperpoverkhnostei”, Matem. sb., 28 (1951), 635–640 | MR | Zbl

[10] J. Milnor, “On the Betti numbers of real varieties”, Proc. Amer. Math. Soc., 15 (1964), 275–280 | DOI | MR | Zbl

[11] R. Thom, “Sur l'homologie des variétés algébriques réelles”, Differential and Combinatorial Topology, A symposium in honour of Marston Morse, Princeton Univ. Press, Princeton, 1965, 255–265 | MR | Zbl

[12] A. G. Vitushkin, “K trinadtsatoi probleme Gilberta”, Dokl. AN SSSR, 95:4 (1954), 701–704 | MR | Zbl

[13] A. G. Vitushkin, “Nekotorye otsenki iz teorii tabulirovaniya”, Dokl. AN SSSR, 114:5 (1957), 923–926 | MR | Zbl

[14] A. N. Kolmogorov, “Otsenki chisla elementov $\varepsilon$-setei v razlichnykh funktsionalnykh klassakh i ikh primenenie k voprosu o predstavimosti funktsii neskolkikh peremennykh superpozitsiyami funktsii menshego chisla peremennykh”, UMN, 10:1 (1955), 192–194 | Zbl

[15] A. G. Khovanskij, Fewnomials, Transl. Math. Monogr., 88, Amer. Math. Soc., Providence, RI, 1991 ; Malochleny, Fazis, M., 1997 | Zbl | MR

[16] V. I. Arnold, “Indeks osoboi tochki vektornogo polya, neravenstva Petrovskogo–Oleinik i smeshannye struktury Khodzha”, Funkts. analiz i ego pril., 12:1 (1978), 1–14 | MR | Zbl

[17] Zadachi Arnolda, Fazis, M., 2000, zadacha 1985-13, s. 61 | MR

[18] I. M. Gelfand, M. M. Kapranov, A. V. Zelevinsky, Determinants, Resultants, and Multidimensional Determinants, Birkhäuser, Boston, MA, 1994 | MR

[19] V. I. Arnold, “O klassakh kogomologii algebraicheskikh funktsii, sokhranyayuschikhsya pri preobrazovaniyakh Chirngauzena”, Funkts. analiz i ego pril., 4:1 (1970), 84–85 | MR | Zbl

[20] V. Ya. Lin, “Superpozitsii algebraicheskikh funktsii”, Funkts. analiz i ego pril., 10:1 (1976), 37–45 | MR | Zbl

[21] I. G. Petrowsky, “On the diffusion of waves and the lakunas for hyperbolic equations”, Matem. sb., 17:3 (1945), 289–370 | MR | Zbl

[22] A. N. Kolmogorov, I. G. Petrovskii, N. S. Piskunov, “Issledovanie uravneniya diffuzii, soedinennoi s vozrastaniem kolichestva veschestva, i ego primenenie k odnoi biologicheskoi zadache”, Byull. MGU, matem., mekh., 1:6 (1937), 1–26 | MR

[23] M. Atiyah, R. Bott, L. Garding, “Lakuna for hyperbolic differential operators with constant coefficients. I”, Acta Math., 124 (1970), 109–189 | DOI | MR | Zbl

[24] M. Atiyah, R. Bott, L. Garding, “Lakuna for hyperbolic differential operators with constant coefficients. II”, Acta Math., 131 (1973), 145–206 | DOI | MR | Zbl

[25] V. A. Vasilev, “Rezkost i lokalnoe uslovie Petrovskogo dlya strogo giperbolicheskikh uravnenii s postoyannymi koeffitsientami”, Izv. AN SSSR. Ser. matem., 50:2 (1986), 242–283 | MR

[26] V. A. Vasilev, “Geometriya lokalnykh lakun dlya giperbolicheskikh uravnenii s postoyannymi koeffitsientami”, Matem. sb., 183:1 (1992), 114–129 | MR | Zbl

[27] V. A. Vasil'ev, “Local Petrovsky lakunas”, Encyclopaedia of Mathematical Sciences, 39, ed. V. I. Arnold, Springer-Verlag, Berlin, 1993, 173–217