Structurally stable configurations of lines of principal curvature
Bifurcation, théorie ergodique et applications - 22-26 juin 1981, Astérisque, no. 98-99 (1982), 21 p.
@incollection{AST_1983__98-99__195_0,
     author = {Sotomayor, J. and Gutierrez, C.},
     title = {Structurally stable configurations of lines of principal curvature},
     booktitle = {Bifurcation, th\'eorie ergodique et applications - 22-26 juin 1981},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {98-99},
     year = {1982},
     zbl = {0521.53003},
     mrnumber = {724448},
     language = {en},
     url = {http://archive.numdam.org/item/AST_1983__98-99__195_0/}
}
TY  - CHAP
AU  - Sotomayor, J.
AU  - Gutierrez, C.
TI  - Structurally stable configurations of lines of principal curvature
BT  - Bifurcation, théorie ergodique et applications - 22-26 juin 1981
AU  - Collectif
T3  - Astérisque
PY  - 1982
DA  - 1982///
IS  - 98-99
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_1983__98-99__195_0/
UR  - https://zbmath.org/?q=an%3A0521.53003
UR  - https://www.ams.org/mathscinet-getitem?mr=724448
LA  - en
ID  - AST_1983__98-99__195_0
ER  - 
Sotomayor, J.; Gutierrez, C. Structurally stable configurations of lines of principal curvature, dans Bifurcation, théorie ergodique et applications - 22-26 juin 1981, Astérisque, no. 98-99 (1982), 21 p. http://archive.numdam.org/item/AST_1983__98-99__195_0/

[1] Berry M; Hannay J.: Umbilic points on Gaussian random surfaces; J. Phys. A. Vol 10, N° 11, 1977. | Article | Zbl 0445.53002

[2] Cayley A. : On differential equations and umbilici; Philos. Mag., Vol. 26, 1863, 373-379, 441-452, (Collected Works, Vol. V). | Article

[3] Darboux G. : Sur la forme des lignes de courbure dans le voisinage d'un ombilic, Note VII, Leçons sur la théorie générale des surfaces. Vol. IV. Gauthier-Villars. 1896. | MR 1365962

[4] Gullstrand A.: Zur Kenntniss der Kreispunkte, Acta Math. Vol. 29, 1905. | Article | JFM 35.0614.01 | MR 1555011

[5] Gutiérrez C; Sotomayor J.: An approximation theorem for immersions with stable configurations of lines of principal curvature. To appear, Proc. International Symp. on Dynamical Systems, IMPA, 1981. | MR 730276 | Zbl 0528.53002

[6] Hamburger H.: Beweis einer Caratheodoryschen Vermutung, Acta. Math. Vol. 73; 1941; 175-228, 229-332. | Article | JFM 67.0696.01 | MR 6481 | Zbl 0025.42404

[7] Hartman P., Wintner A.: On the singularities in nets of curves defined by differential equations. Amer. Jour. Math. Vol. 75, 1953, 277-297. | Article | MR 55007 | Zbl 0053.29304

[8] Klotz T.: On Bol's Proof of Caratheodory' s Conjecture, Comm. Pure and Appl. Math. Vol. 12. 1959, 277-311. | Article | MR 120602 | Zbl 0091.34301

[9] Peixoto M. C.; Peixoto M.: Structural stability in the plane with enlarged boundary conditions. An. Acad. Bras. Ciencias, Vol. 31, 1959. | MR 107067 | Zbl 0107.07102

[10] Picard E.: Traité d'analyse, Vol. 3, Gauthier Villars, 1904. | JFM 40.0330.15

[11] Porteus I. R.: The normal singularities of a submanifold. J. Diff. Geom. Vol. 5. 1971. | MR 292092 | Zbl 0226.53010

[12] Struik D.: Lectures on classical differential geometry, Addisson Wesley, 1950. | MR 36551 | Zbl 0105.14707

[13] Thom R.: Stabilité Structurelle et Morphogénèse. Benjamin, 1972. | MR 488155 | Zbl 0294.92001