An example of a wild strange attractor

Sbornik Mathematics

Volumn 189, Issue 1-2, 1998, Pages 291-314

  Turaev, D V ^a   Shi'nikov, L P ^b  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b Res Inst Appl Math and Cybernet   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032220873     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/sm1998v189n02abeh000300     Document Type: Article

References (32)

1. S. E. Newhouse, "The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms", Inst. Hautes Études Sci. Publ. Math. 50 (1979), 101-151.
2. S. E. Newhouse, "Diffeomorphisms with infinitely many sinks", Topology 13 (1974), 9-18.
3. S. V. Gonchenko, L. P. Shil'nikov, and D. V. Turaev, "On models with non-rough Poincaré homoclinic curves", Phys. D 62:1-4 (1993), 1-14.
4. S. V. Gonchenko, D. V. Turaev, and L. P. Shil'nikov, "Dynamical phenomena in multidimensional systems with a non-transversal homoclinic Poincaré curve", Ross. Akad. Nauk Dokl. 330 (1993), 144-147; English transl. in Russian Acad. Sci. Dokl. Math. 47 (1993).
5. S. V. Gonchenko, D. V. Turaev, and L. P. Shil'nikov, "Dynamical phenomena in multidimensional systems with a non-transversal homoclinic Poincaré curve", Ross. Akad. Nauk Dokl. 330 (1993), 144-147; English transl. in Russian Acad. Sci. Dokl. Math. 47 (1993).
6. S. V. Gonchenko, L. P. Shil'nikov, and D. V. Turaev, "Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits", Chaos 6 (1996), 15-31.
7. V. S. Afraimovich, V. V. Bykov, and L. P. Shil'nikov, "On the appearance and structure of Lorenz attractors", Dokl. Akad. Nauk SSSR 234 (1977), 336-339; English transl. in Soviet Math. Dokl. 18 (1977).
8. V. S. Afraimovich, V. V. Bykov, and L. P. Shil'nikov, "On the appearance and structure of Lorenz attractors", Dokl. Akad. Nauk SSSR 234 (1977), 336-339; English transl. in Soviet Math. Dokl. 18 (1977).
9. V. S. Afraimovich, V. V. Bykov, and L. P. Shil'nikov, "On structurally unstable attracting limit sets of the Lorenz attractor type", Trudy Moskov. Mat. Obshch. 44 (1982), 150-212; English transl. in Trans. Moscow Math. Soc. 1983:2.
10. V. S. Afraimovich, V. V. Bykov, and L. P. Shil'nikov, "On structurally unstable attracting limit sets of the Lorenz attractor type", Trudy Moskov. Mat. Obshch. 44 (1982), 150-212; English transl. in Trans. Moscow Math. Soc. 1983:2.
11. 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).
12. 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).
13. M. W. Hirsh, C. C. Pugh, and M. Shub, "Invariant manifolds", Lecture Notes in Mathematics, vol. 583, Springer-Verlag, Berlin 1977.
14. J. Guckenheimer and R. F. Williams, "Structural stability of Lorenz attractors", Astérisque 50 (1979), 307-320.
15. D. V. Anosov, "Geodesic flows on closed Riemannian manifolds of negative curvature", Trudy Inst. Mat. Steklov. 90 (1967); English transl. in Proc. Steklov Inst. Math. 90 (1969).
16. D. V. Anosov, "Geodesic flows on closed Riemannian manifolds of negative curvature", Trudy Inst. Mat. Steklov. 90 (1967); English transl. in Proc. Steklov Inst. Math. 90 (1969).
17. Ya. B. Pesin, "Characteristic Lyapunov exponents and smooth ergodic theory", Uspekhi Mat. Nauk 32:4 (1977), 55-111; English transl. in Russian Math. Surveys 32:4 (1977).
18. Ya. B. Pesin, "Characteristic Lyapunov exponents and smooth ergodic theory", Uspekhi Mat. Nauk 32:4 (1977), 55-111; English transl. in Russian Math. Surveys 32:4 (1977).
19. D. V. Anosov, S. Kh. Aranson, I. U. Bronshtein, and V. Z. Grines, "Smooth dynamical systems. II", Itogi Nauki i Tekhniki: Sovrem. Probl. Mat.: Fund. Naprav., vol. 1, VINITI, Moscow 1985, pp. 151-242; English transl., Encyclopaedia Math. Sci., vol. 1 [Dynamical Systems, I], Springer-Verlag, Berlin 1988.
20. D. V. Anosov, S. Kh. Aranson, I. U. Bronshtein, and V. Z. Grines, "Smooth dynamical systems. II", Itogi Nauki i Tekhniki : Sovrem. Probl. Mat.: Fund. Naprav., vol. 1, VINITI, Moscow 1985, pp. 151-242; English transl., Encyclopaedia Math. Sci., vol. 1 [Dynamical Systems, I], Springer-Verlag, Berlin 1988.
21. J. Auslander, "Generalized recurrence in dynamical systems", Contributions to differential equations, vol. 3, John Wiley and Sons, Inc., New York 1964, pp. 65-74.
22. L. P. Shil'nikov, "On the question of the structure of an extended neighbourhood of a structurally stable equilibrium state of saddle-focus type", Mat. Sb. 81 (123) (1970), 92-113; English transl. in Math. USSR Sb. 10 (1970).
23. L. P. Shil'nikov, "On the question of the structure of an extended neighbourhood of a structurally stable equilibrium state of saddle-focus type", Mat. Sb. 81 (123) (1970), 92-113; English transl. in Math. USSR Sb. 10 (1970).
24. S. V. Gonchenko, D. V. Turaev, and L. P. Shil'nikov, "On the existence of Newhouse regions near systems with a non-transversal homoclinic Poincaré curve (the multidimensional case)", Ross. Akad. Nauk Dokl. 329 (1993), 404-407; English transl. in Russian Acad. Sci. Dokl. Math. 47 (1993).
25. S. V. Gonchenko, D. V. Turaev, and L. P. Shil'nikov, "On the existence of Newhouse regions near systems with a non-transversal homoclinic Poincaré curve (the multidimensional case)", Ross. Akad. Nauk Dokl. 329 (1993), 404-407; English transl. in Russian Acad. Sci. Dokl. Math. 47 (1993).
26. J. Palis and M. Viana, "High-dimension diffeomorphisms displaying infinitely many periodic attractors", Ann. of Math. (2) 140 (1994), 207-250.
27. 1-stability conjecture for flow", Preprint.
28. J. A. Feroe, "Homoclinic orbits in a parametrized saddle-focus system", Phys. D 62:1-4 (1993), 254-262.
29. L. P. Shil'nikov, "On a problem of Poincaré and Birkhoff", Mat. Sb. 74 (116) (1967), 378-397; English transl. in Math. USSR Sb. 3 (1967).
30. L. P. Shil'nikov, "On a problem of Poincaré and Birkhoff", Mat. Sb. 74 (116) (1967), 378-397; English transl. in Math. USSR Sb. 3 (1967).
31. D. V. Turaev, "On dimension of non-local bifurcational problems", Internat. J. Bifur. Chaos Appl. Sci. Engrg. 6 (1996), 919-948.
32. B. Sandstede, "Center manifolds for homoclinic solutions", Preprint, 1994.