Geodesic
Two-mode branching of ferroelectric phase heterogeneous crystals of singular phase of the sixth order
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 11 (2009), pp. 37-47 
I. V. Kolesnikova; Yu. I. Sapronov. Two-mode branching of ferroelectric phase heterogeneous crystals of singular phase of the sixth order. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 11 (2009), pp. 37-47. http://geodesic.mathdoc.fr/item/VCHGU_2009_11_a3/
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     title = {Two-mode branching of ferroelectric phase heterogeneous crystals of singular phase of the sixth order},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {37--47},
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     number = {11},
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     url = {http://geodesic.mathdoc.fr/item/VCHGU_2009_11_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A description of the distribution of extremals of Fredholm functionals bifurcation points of the minima of 2-dimensional features of degeneration and the sixth order. The main illustrating example is the task of branching ferroelectric phase heterogeneous crystals. We use a modified the Lyapunov—Schmidt method, equipped with the elements of the theory of singularities of smooth functions.

[1] Yu. A. Izyumov, V. I. Syromyatnikov, Fazovye perekhody i simmetriya kristallov, Nauka, M., 1984, 247 pp.

[2] V. B. Shirokov, Yu. I. Yuzyuk, B. Dkhil, V. V. Lemanov, “Fenomenologicheskoe opisanie fazovykh perekhodov v tonkikh plenkakh V.N. $BaTiO_3$”, Fizika tverdogo tela, 50:5 (2008), 889–892

[3] M. A. Krasnoselskii, N. A. Bobylev, E. M. Mukhamadiev, “Ob odnoi skheme issledovaniya vyrozhdennykh ekstremalei funktsionalov klassicheskogo variatsionnogo ischisleniya”, DAN SSSR, 240:3 (1978), 530–533 | MR

[4] B. M. Darinskii, Yu. I. Sapronov, S. L. Tsarev, “Bifurkatsii ekstremalei fredgolmovykh funktsionalov”, Sovremennaya matematika. Fundamentalnye napravleniya, 12 (2004), 3–140 | Zbl

[5] Yu. G. Borisovich, V. G. Zvyagin, Yu. I. Sapronov, “Nelineinye fredgolmovy otobrazheniya i teoriya Lere — Shaudera”, Uspekhi mat. nauk, 32:4 (1977), 3–54 | MR | Zbl

[6] V. I. Arnold, A. N. Varchenko, S. M. Gusein-Zade, Osobennosti differentsiruemykh otobrazhenii, MTsNMO, M., 2004, 672 pp. | MR

[7] T. Poston, I. Styuart, Teoriya katastrof i eë prilozheniya, Mir, M., 1980, 608 pp. | MR

[8] T. Breker, L. Lander, Differentsiruemye rostki i katastrofy, Mir, M., 1977, 208 pp.

[9] V. Poénaru, “Singularités $C^{\infty}$ en Présence de Symétrie”, Lecture Notes in Mathematics, 510, chapter II, Springer-Verlag, N.-Y., 1976, 61—89 | MR

[10] Yu. I. Sapronov, “Poluregulyarnye uglovye osobennosti gladkikh funktsii”, Mat. sb., 180:10 (1989), 1299—1310

[11] M. A. Khussain, “K diskriminantnomu analizu bifurkatsii ravnovesii uprugoi balki s dvumya poluogranichitelyami”, Tr. mat. f-ta, no. 8, VorGU, Voronezh, 2004, 102—107

[12] A. V. Beloglazov, “Bifurkatsii ekstremalei fredgolmova funktsionala iz ombilicheskoi tochki minimuma v vershine ugla”, Vestn. VGU.— Ser. Fizika. Matematika, 2006, no. 2, 147—153

[13] M. M. Postnikov, Vvedenie v teoriyu Morsa, Nauka, M., 1971, 568 pp. | MR