On the complex bifurcation set for a system with simple dynamics

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 6, Issue 5, 1996, Pages 949-968

  Shashkov, Mikhail V ^a   Turaev, Dmitry V ^a  

^a Institute for Applied Mathematics and Cybernetics   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030136341     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127496000527     Document Type: Article

References (23)

1. Chow, S. N., Deng, B. & Terman, D. [1990] "The bifurcation of homoclinic and periodic orbits from two heteroclinic orbits," SIAM J. Math. Anal. 21, 179-204.
2. Gonchenko, S. V., Shil'nikov, L. P. & Turaev, D. V. [1991] "On models with a structurally unstable homoclinic curve," Dokl. Acad. Nauk USSR 320, 269-272; English translation in [1992] Sov. Math. Dokl. 44, 422-426.
3. Gonchenko, S. V., Shil'nikov, L. P. & Turaev, D. V. [1991] "On models with a structurally unstable homoclinic curve," Dokl. Acad. Nauk USSR 320, 269-272; English translation in [1992] Sov. Math. Dokl. 44, 422-426.
4. Gonchenko, S. V., Shil'nikov, L. P. & Turaev, D. V. [1993] "On models with a non-rough Poincaré homoclinic curve," Physica D62, 1-14.
5. Hirsch, M., Pugh, C. & Shub, M. [1977] "Invariant manifolds," Lecture Notes in Mathematics, Vol. 583 (Springer-Verlag).
6. Homburg, A. J. [1993] "Some global aspects of homoclinic bifurcations of vector fields," preprint.
7. Ovsyannikov, I. M. & Shil'nikov, L. P. [1986] "On systems with a saddle-focus homoclinic curve," Mat. Sb. 130, 552-570; English translation in [1987] Math. USSR Sb. 58, 557-574.
8. Ovsyannikov, I. M. & Shil'nikov, L. P. [1986] "On systems with a saddle-focus homoclinic curve," Mat. Sb. 130, 552-570; English translation in [1987] Math. USSR Sb. 58, 557-574.
9. Ovsyannikov, I. M. & Shil'nikov, L. P. [1991] "Systems with a homoclinic curve of multidimensional saddle-focus type, and spiral chaos," Mat. Sb. 182, 1043-1073; English translation in [1992] Math. USSR Sb. 73, 415-443.
10. Ovsyannikov, I. M. & Shil'nikov, L. P. [1991] "Systems with a homoclinic curve of multidimensional saddle-focus type, and spiral chaos," Mat. Sb. 182, 1043-1073; English translation in [1992] Math. USSR Sb. 73, 415-443.
11. Sandstede, B. [1994] "Center manifolds for homoclinic solutions," preprint.
12. Shashkov, M. V. [1991] "On existence of a smooth invariant two-dimensional attractive manifold for systems with a separatrix contour," in Methods of Qualitative Theory and Theory of Bifurcations (Nizhny Novgorod State University), pp. 61-73 (in Russian).
13. Shashkov, M. V., Shil'nikov, L. P. & Turaev, D. V. [1995] "On existence of a smooth invariant manifold for systems with a heteroclinic contour," to appear.
14. Shil'nikov, L. P. [1963] "Some cases of generation of periodic motion from singular trajectories," Mat. Sb. 61, 443-466 (in Russian).
15. Shil'nikov, L. P. [1965] "A case of the existence of a denumerable set of periodic motions," Dokl. Acad. Nauk USSR 160, 558-561; English translation in [1965] Sov. Math. Dokl. 6, 163-166.
16. Shil'nikov, L. P. [1965] "A case of the existence of a denumerable set of periodic motions," Dokl. Acad. Nauk USSR 160, 558-561; English translation in [1965] Sov. Math. Dokl. 6, 163-166.
17. Shil'nikov, L. P. [1967] "On a Poincaré-Birkhoff problem," Mat. Sb. 74, 378-397; English translation in [1968] Math. USSR Sb. 3, 415-443.
18. Shil'nikov, L. P. [1967] "On a Poincaré-Birkhoff problem," Mat. Sb. 74, 378-397; English translation in [1968] Math. USSR Sb. 3, 415-443.
19. Shil'nikov, L. P. [1968] "On the generation of a periodic motion from a trajectory doubly asymptotic to an equilibrium state of saddle type," Mat. Sb. 77, 461-472; English translation in [1968] Math. USSR Sb. 6, 415-443.
20. Shil'nikov, L. P. [1968] "On the generation of a periodic motion from a trajectory doubly asymptotic to an equilibrium state of saddle type," Mat. Sb. 77, 461-472; English translation in [1968] Math. USSR Sb. 6, 415-443.
21. Shil'nikov, L. P. [1970] "A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type," Mat. Sb. 81, 92-103; English translation in [1970] Math. USSR Sb. 10, 91-102.
22. Shil'nikov, L. P. [1970] "A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type," Mat. Sb. 81, 92-103; English translation in [1970] Math. USSR Sb. 10, 91-102.
23. Turaev, D. V. [1984] "On a case of bifurcations of a contour composed by two homoclinic curves of a saddle," in Methods of Qualitative Theory of Differential Equations (Gorky State University), pp. 162-175 (in Russian).