Geodesic
A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type
Sbornik. Mathematics, Tome 10 (1970) no. 1, pp. 91-102 
L. P. Shilnikov. A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type. Sbornik. Mathematics, Tome 10 (1970) no. 1, pp. 91-102. http://geodesic.mathdoc.fr/item/SM_1970_10_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that in a neighborhood of a trajectory which is doubly asymptotic to a rough state of equilibrium of saddle-focus type, under addition assumptions on the dynamical system, there exists a subsystem whose trajectories are in one-to-one correspondence with a set which is the quotient space of a topological Bernoulli process with an infinite set of symbols. Bibliography: 10 titles.

[1] S. Smeil, “Strukturno ustoichivyi differentsiruemyi gomeomorfizm s beskonechnym chislom periodicheskikh tochek”, Trudy mezhdunarodnogo simpoziuma po nelineinym kolebaniyam, t. 2, Kiev, 1963, 365–366

[2] L. P. Shilnikov, “Ob odnom sluchae suschestvovaniya schetnogo mnozhestva periodicheskikh dvizhenii”, DAN SSSR, 160:3 (1965), 558–561

[3] L. P. Shilnikov, “O suschestvovanii schetnogo mnozhestva periodicheskikh dvizhenii v chetyrekhmernom prostranstve v rasshirennoi okrestnosti sedlo-fokusa”, DAN SSSR, 172:1 (1967), 54–57

[4] L. P. Shilnikov, “Ob odnoi zadache Puankare–Birkgofa”, Matem. sb., 74(116) (1967), 378–397

[5] S. Smale, Diffeomorptiisms wiht many periodic points, Differential and combinatorial topology, Princeton, 1965

[6] L. P. Shilnikov, “K voprosu o strukture okrestnosti gomoklinicheskoi truby invariantnogo tora”, DAN SSSR, 180:2 (1968), 286–1289

[7] L. P. Shilnikov, “O rozhdenii periodicheskogo dvizheniya iz traektorii, dvoyakoasimptoticheskoi k sostoyaniyu ravnovesiya tipa sedlo”, Matem. sb., 77(119) (1968), 461–472

[8] Yu. I. Neimark, L. P. Shilnikov, “Ob odnom sluchae rozhdeniya periodicheskikh dvizhenii”, DAN SSSR, 160:6 (1965), 1261–1264 | MR | Zbl

[9] V. P. Grigorenko, “Ob odnom sluchae schetnogo chisla periodicheskikh dvizhenii u releinoi sistemy”, izv. VUZov, Radiofizika, 10:3 (1967), 340–344

[10] L. P. Shilnikov, “Ob odnom novom tipe bifurkatsii mnogomernykh dinamicheskikh sistem”, DAN SSSR (to appear)