Moduli of Ω-conjugacy of two-dimensional diffeomorphisms with a structurally unstable heteroclinic contour

Sbornik Mathematics

Volumn 187, Issue 9-10, 1996, Pages 1261-1281

  Gonchenko, S V ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030527008     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/SM1996v187n09ABEH000155     Document Type: Article

References (33)

1. J. Palis, "A differentiable invariant of topological conjugacies and moduli of stability", Astérisque 51 (1978), 335-346.
2. S. V. Gonchenko, "Moduli of systems with structurally unstable homoclinic orbits (the cases of diffeomorphisms and vector fields)", Methods in qualitative theory and bifurcation theory (L. P. Shil'nikov, ed.). Gor'kov. Gos. Univ., Gorky 1989, pp. 34-49; English transl. in Selecta Math. Sovietica 11 (1992).
3. S. V. Gonchenko, "Moduli of systems with structurally unstable homoclinic orbits (the cases of diffeomorphisms and vector fields)", Methods in qualitative theory and bifurcation theory (L. P. Shil'nikov, ed.). Gor'kov. Gos. Univ., Gorky 1989, pp. 34-49; English transl. in Selecta Math. Sovietica 11 (1992).
4. S. V. Gonchenko and L. P. Shil'nikov, "Ω-conjugacy invariants of diffeomorphisms with a structurally unstable homoclinic trajectory", Ukrain. Mat. Zh. 42 (1990), 153-159; English transl. in Ukrainian Math. J. 42 (1990).
5. S. V. Gonchenko and L. P. Shil'nikov, "Ω-conjugacy invariants of diffeomorphisms with a structurally unstable homoclinic trajectory", Ukrain. Mat. Zh. 42 (1990), 153-159; English transl. in Ukrainian Math. J. 42 (1990).
6. S. V. Gonchenko and L. P. Shil'nikov, "On moduli of systems with a structurally unstable homoclinic Poincaré curve", Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992), 1165-1197; English transl. in Russian Acad. Sci. Izv. Math. 41 (1993).
7. S. V. Gonchenko and L. P. Shil'nikov, "On moduli of systems with a structurally unstable homoclinic Poincaré curve", Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992), 1165-1197; English transl. in Russian Acad. Sci. Izv. Math. 41 (1993).
8. S. V. Gonchenko, D. V. Turaev, and L. P. Shil'nikov, "On models with a structurally unstable homoclinic Poincaré curve", Dokl. Akad. Nauk SSSR 320 (1991), 269-272; English transl. in Soviet Math. Dokl. 44 (1992).
9. S. V. Gonchenko, D. V. Turaev, and L. P. Shil'nikov, "On models with a structurally unstable homoclinic Poincaré curve", Dokl. Akad. Nauk SSSR 320 (1991), 269-272; English transl. in Soviet Math. Dokl. 44 (1992).
10. S. V. Gonchenko, L. P. Shil'nikov, and D. V. Turaev. "On models with non-rough Poincaré homoclinic curves", Phys. D 62 (1993), 1-14.
11. N. K. Gavrilov and L. P. Shil'nikov, "On three-dimensional dynamical systems close to a system with a structurally unstable homoclinic curve", I, II, Mat. Sb. 88 (1972), 475-492, and 90 (1973), 139-157; English transl. in Math USSR-Sb. 17 (1972) and 19 (1973).
12. N. K. Gavrilov and L. P. Shil'nikov, "On three-dimensional dynamical systems close to a system with a structurally unstable homoclinic curve", I, II, Mat. Sb. 88 (1972), 475-492, and 90 (1973), 139-157; English transl. in Math USSR-Sb. 17 (1972) and 19 (1973).
13. N. K. Gavrilov and L. P. Shil'nikov, "On three-dimensional dynamical systems close to a system with a structurally unstable homoclinic curve", I, II, Mat. Sb. 88 (1972), 475-492, and 90 (1973), 139-157; English transl. in Math USSR-Sb. 17 (1972) and 19 (1973).
14. N. K. Gavrilov and L. P. Shil'nikov, "On three-dimensional dynamical systems close to a system with a structurally unstable homoclinic curve", I, II, Mat. Sb. 88 (1972), 475-492, and 90 (1973), 139-157; English transl. in Math USSR-Sb. 17 (1972) and 19 (1973).
15. S. V. Gonchenko, "Non-trivial hyperbolic subsets of systems with a structurally unstable homoclinic curve", Methods of the qualitative theory of differential equations, (E. A. Leontovich-Andronova, ed.), Gor'kov. Gos. Univ., Gorky 1984, pp. 89-102. (Russian).
16. S. V. Gonchenko and L. P. Shil'nikov, "On dynamical systems with structurally unstable homoclinic curves", Dokl. Akad. Nauk SSSR 286 (1986), 1049-1053; English transl. in Soviet Math. Dokl. 33 (1986).
17. S. V. Gonchenko and L. P. Shil'nikov, "On dynamical systems with structurally unstable homoclinic curves", Dokl. Akad. Nauk SSSR 286 (1986), 1049-1053; English transl. in Soviet Math. Dokl. 33 (1986).
18. L. P. Shil'nikov, "On a Poincaré-Birkhoff problem", Mat. Sb. 74 (116) (1967), 378-397; English transl. in Math. USSR-Sb. 3 (1967).
19. L. P. Shil'nikov, "On a Poincaré-Birkhoff problem", Mat. Sb. 74 (116) (1967), 378-397; English transl. in Math. USSR-Sb. 3 (1967).
20. N. K. Gavrilov, "Three-dimensional dynamical systems with a structurally unstable homoclinic contour", Mat. Zometki 14 (1973), 687-696; English transl. in Math. Notes 14 (1973).
21. N. K. Gavrilov, "Three-dimensional dynamical systems with a structurally unstable homoclinic contour", Mat. Zometki 14 (1973), 687-696; English transl. in Math. Notes 14 (1973).
22. L. P. Shil'nikov, "A case of the existence of a countable number of periodic motions", Dokl. Akad. Nauk SSSR 160 (1965), 558-561; English transl. in Soviet Math. Dokl. 6 (1965).
23. L. P. Shil'nikov, "A case of the existence of a countable number of periodic motions", Dokl. Akad. Nauk SSSR 160 (1965), 558-561; English transl. in Soviet Math. Dokl. 6 (1965).
24. V. I. Arnol'd, V. S. Afraimovich, Yu. S. Il'yashenko, and L. P. Shil'nikov, Bifurcation theory, Itogi Nauki i Tekhniki: Sovrem. Probl. Mat.: Fund. Naprav., vol. 5, Moscow, VINITI, 1986, 5-218; English transl. in Encyclopaedia Math. Sci., vol. 5 [Dynamical Systems, V], Springer-Verlag, Berlin 1995.
25. V. I. Arnol'd, V. S. Afraimovich, Yu. S. Il'yashenko, and L. P. Shil'nikov, Bifurcation theory, Itogi Nauki i Tekhniki: Sovrem. Probl. Mat.: Fund. Naprav., vol. 5, Moscow, VINITI, 1986, 5-218; English transl. in Encyclopaedia Math. Sci., vol. 5 [Dynamical Systems, V], Springer-Verlag, Berlin 1995.
26. Y. Togawa, "A modulus of 3-dimensional vector fields", Ergodic Theory Dynamical Systems 7 (1987), 295-301.
27. L. P. Shil'nikov, "On the problem of the structure of an extended neighbourhood of a structurally stable equilibrium state of saddle-focus type", Mat. Sb. 81 (123) (1970), 92-103; English transl. in Math. USSR-Sb. 10 (1970).
28. L. P. Shil'nikov, "On the problem of the structure of an extended neighbourhood of a structurally stable equilibrium state of saddle-focus type", Mat. Sb. 81 (123) (1970), 92-103; English transl. in Math. USSR-Sb. 10 (1970).
29. I. M. Ovsyannikov and L. P. Shil'nikov, "On systems with a saddle-focus homoclinic curve", Mat. Sb. 130 (172) (1986), 552-570; English transl. in Math. USSR-Sb. 58 (1987).
30. I. M. Ovsyannikov and L. P. Shil'nikov, "On systems with a saddle-focus homoclinic curve", Mat. Sb. 130 (172) (1986), 552-570; English transl. in Math. USSR-Sb. 58 (1987).
31. I. M. Ovsyannikov and L. P. Shil'nikov, "Systems with a homoclinic curve of multidimensional saddle-focus type, and spiral chaos", Mat. Sb. (182) (1991), 1043-1073; English transl. in Math. USSR-Sb. 73 (1992).
32. I. M. Ovsyannikov and L. P. Shil'nikov, "Systems with a homoclinic curve of multidimensional saddle-focus type, and spiral chaos", Mat. Sb. (182) (1991), 1043-1073; English transl. in Math. USSR-Sb. 73 (1992).
33. S. V. Gonchenko, "On the question of conditions for the conjugacy of two-dimensional homeomorphisms with a structurally unstable homoclinic trajectory", in Methods of qualitative theory and bifurcation theory, Gor'kov. Gos. Univ., Gorky 1990, pp. 5-19. (Russian).