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Simultaneous continuation of infinitely many sinks at homoclinic bifurcations
1. | Instituto de Matemática y Estadística Prof. Rafael Laguardia (IMERL), Facultad de Ingeniería, Universidad de la República, Uruguay |
2. | Instituto de Matemática y Estadistica Prof. Rafael Laguardia (IMERL), Facultad de Ingeniería, Universidad de la República, Uruguay |
3. | Instituto de Matemática y Estadistica Prof. Rafael Laguardia (IMERL), Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay |
References:
[1] |
E. Colli, Infinitely many coexisting strange attractors, Annales de l'I.H.P. Analyse non-linéaire, 15 (1998), 539-579. |
[2] |
M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds," Lecture Notes in Mathematics, 583, Springer-Verlag, Berlin-New York, 1977. |
[3] |
W. de Melo, Structural stability of diffeomorphisms on two-manifolds, Inventiones Math, 21 (1973), 233-246.
doi: 10.1007/BF01390199. |
[4] |
A. Gorodetski and V. Kaloshin, How often surface diffeomorphisms have inifinitely sinks and hyperbolicity of periodic points near an homoclinic tangency, Adv. Math., 208 (2007), 710-797.
doi: 10.1016/j.aim.2006.03.012. |
[5] |
I. Kan, H. Koçak and J. A. Yorke, Antimonotonicity: Concurrent creation and annihilation of periodic orbits, Ann. Math., 136 (1992), 219-252.
doi: 10.2307/2946605. |
[6] |
S. Newhouse, Non density of Axiom A on $S^2$, Proc. A.M.S. Symp. Pure Math., 14 (1970), 191-202.
doi: 10.1016/0040-9383(74)90034-2. |
[7] |
S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology, 13 (1974), 9-18. |
[8] |
S. Newhouse, The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms, Publ. IHÉS, 50 (1979), 101-151. |
[9] |
J. Palis, A global view of dynamics and a conjecture on the denseness of finitude of attractors. Géométrie complexe et systèmes dynamiques (Orsay, 1995), Astérisque, 261 (2000), 335-347. |
[10] |
J. Palis and F. Takens, "Hyperbolicity and Sensitive Chaotic Dynanics of Homoclinic Bifurcations," University Press, Cambridge, 1993. |
[11] |
C. Robinson, Bifurcation to infinitely many sinks, Comm Math Phys., 90 (1983), 433-459.
doi: 10.1007/BF01206892. |
[12] |
M. Shub, "Global Stability of Dynamical Systems," Springer Verlag, Berlin, New York, (1987), 23-27. |
[13] |
S. Smale, Diffeomorphisms with many periodic points, in " Differential and Combinatorial Topology," Princeton Univ. Press, (1965), 63-80. |
[14] |
L. Tedeschini-Lalli and J. A. Yorke, How often do simple dynamical processes have infinitely many coexisting sinks?, Comm. Math. Phys., 106 (1986), 635-657.
doi: 10.1007/BF01463400. |
[15] |
J. A. Yorke and K. T. Alligood, Cascades of period doubling bifurcations: A prerequisite for horseshoes, Bull AMS, 9 (1983), 319-322.
doi: 10.1090/S0273-0979-1983-15191-1. |
show all references
References:
[1] |
E. Colli, Infinitely many coexisting strange attractors, Annales de l'I.H.P. Analyse non-linéaire, 15 (1998), 539-579. |
[2] |
M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds," Lecture Notes in Mathematics, 583, Springer-Verlag, Berlin-New York, 1977. |
[3] |
W. de Melo, Structural stability of diffeomorphisms on two-manifolds, Inventiones Math, 21 (1973), 233-246.
doi: 10.1007/BF01390199. |
[4] |
A. Gorodetski and V. Kaloshin, How often surface diffeomorphisms have inifinitely sinks and hyperbolicity of periodic points near an homoclinic tangency, Adv. Math., 208 (2007), 710-797.
doi: 10.1016/j.aim.2006.03.012. |
[5] |
I. Kan, H. Koçak and J. A. Yorke, Antimonotonicity: Concurrent creation and annihilation of periodic orbits, Ann. Math., 136 (1992), 219-252.
doi: 10.2307/2946605. |
[6] |
S. Newhouse, Non density of Axiom A on $S^2$, Proc. A.M.S. Symp. Pure Math., 14 (1970), 191-202.
doi: 10.1016/0040-9383(74)90034-2. |
[7] |
S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology, 13 (1974), 9-18. |
[8] |
S. Newhouse, The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms, Publ. IHÉS, 50 (1979), 101-151. |
[9] |
J. Palis, A global view of dynamics and a conjecture on the denseness of finitude of attractors. Géométrie complexe et systèmes dynamiques (Orsay, 1995), Astérisque, 261 (2000), 335-347. |
[10] |
J. Palis and F. Takens, "Hyperbolicity and Sensitive Chaotic Dynanics of Homoclinic Bifurcations," University Press, Cambridge, 1993. |
[11] |
C. Robinson, Bifurcation to infinitely many sinks, Comm Math Phys., 90 (1983), 433-459.
doi: 10.1007/BF01206892. |
[12] |
M. Shub, "Global Stability of Dynamical Systems," Springer Verlag, Berlin, New York, (1987), 23-27. |
[13] |
S. Smale, Diffeomorphisms with many periodic points, in " Differential and Combinatorial Topology," Princeton Univ. Press, (1965), 63-80. |
[14] |
L. Tedeschini-Lalli and J. A. Yorke, How often do simple dynamical processes have infinitely many coexisting sinks?, Comm. Math. Phys., 106 (1986), 635-657.
doi: 10.1007/BF01463400. |
[15] |
J. A. Yorke and K. T. Alligood, Cascades of period doubling bifurcations: A prerequisite for horseshoes, Bull AMS, 9 (1983), 319-322.
doi: 10.1090/S0273-0979-1983-15191-1. |
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