Symbolic dynamics in the neighborhood of degenerate homoclinic structures. (English. Russian original) Zbl 0357.34052
Ukr. Math. J. 28(1976), 555-563 (1977); translation from Ukr. Mat. Zh. 28, 723-734 (1976).
MSC:
| 34D30 | Structural stability and analogous concepts of solutions to ordinary differential equations |
References:
| [1] | Yu. I. Neimark, ?Some techniques in the study of dynamical systems,? Proceedings of the Second All-Union Conference on Theoretical and Applied Mechanics [in Russian], Vol. 2, Nauka, Moscow (1985), pp. 97-111. |
| [2] | N. K. Gavrilov and L. P. Shil’nikov, ?On three-dimensional dynamical systems near systems with degenerate homoclinic curves,? Matem. Sb., Pt. 1,88, No. 4, 475-492 (1972); Matem. Sb., Pt. 2,90, No. 1, 139-156 (1973). |
| [3] | V. G. Gruzdev and Yu. I. Neimark, ?On the creation of homoclinic curves through the intersection of integral manifolds,? Abstracts of the All-Union Conference on the Qualitative Theory of Differential Equations, Samarkand (1973), pp. 72-73. |
| [4] | N. K. Gavrilov, ?On three-dimensional dynamical systems with degenerate homoclinic curves,? Mat. Zametki,14, No. 5, 687-696 (1973). |
| [5] | Yu. I. Neimark, ?Symbolic dynamics in the neighborhood of homoclinic structures,? Abstracts of the All-Union Conference on the Qualitative Theory of Differential Equations, Samarkand (1973), pp. 154-155. |
| [6] | Yu. I. Neimark, ?On motions near doubly asymptotic motions,? Dokl, Akad. Nauk SSSR,172, No. 5, 1021-1024 (1967). |
| [7] | Yu. I. Neimark, ?Symbolic dynamics generated by homoclinic structures,? Differents. Uravneniya,12, No. 2, 256-262 (1976). |
| [8] | Yu. I. Neimark, The Method of Point Transformations in the Study of Nonlinear Oscillations [in Russian], Nauka, Moscow (1972). |
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