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Robust attractors without dominated splitting on manifolds with boundary
1. | Departamento de Matemática, Universidad del Bío-Bío, Av. Collao 1202, Casilla 5-C, Concepción, Chile |
2. | Departamento de Matemáticas, Universidad Católica del Norte, Av. Angamos 0610, Casilla 1280, Antofagasta, Chile |
References:
[1] |
V. S. Afraimovich, V. V. Bykov and L. P. Shilnikov, On attracting structurally unstable limit sets of Lorenz attractor type,, Trudy Moskov. Mat. Obshch., 44 (1982), 150.
|
[2] |
V. Araújo and M. J. Pacifico, Three-dimensional Flows, Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series],, 53. Springer, (2010).
doi: 10.1007/978-3-642-11414-4. |
[3] |
R. Bamón, R. Labarca, R. Mańé and M.J. Pacífico, The explosion of singulay cycles,, Inst. Hautes Études Sci. Publ. Math., 78 (1993), 207.
|
[4] |
S. Bautista, The geometric Lorenz attractor is a homoclinic class,, Bol. Mat. (N.S.), 11 (2004), 69.
|
[5] |
C. Bonatti, L. J. Díaz and M. Viana, Dynamics Beyond Uniform Hyperbolicity. A Global Geometric and Probabilistic Perspective, Encyclopaedia of Mathematical Sciences,102, Mathematical Physics III,, Springer-Verlag, (2005).
|
[6] |
D. Carrasco-Olivera, C. A. Morales and B. San Martín, Singular cycles and $C^k$-robust transitive set on manifold with boundary,, Communications in Contemporary Mathematics, 13 (2011), 191.
doi: 10.1142/S0219199711004233. |
[7] |
C. I. Doering, Persistently transitive vector fields on three-dimensional manifolds,, In Procs. on Dynamical Systems and Bifurcations Theory, 160 (1987), 59.
|
[8] |
J. Guckenheimer and R. F. Williams, Structural stability of Lorenz attractors,, Inst. Hautes Études Sci. Publ. Math., 50 (1979), 59.
|
[9] |
M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics,, Vol. 583. Springer-Verlag, (1977).
|
[10] |
M. Milnor, On the concept of attractor,, Comm. Math. Phys., 99 (1985), 177.
doi: 10.1007/BF01212280. |
[11] |
C. A. Morales, Sufficient conditions for a partially hyperbolic attractor to be a homoclinic class,, J. Differential Equations, 249 (2010), 2005.
doi: 10.1016/j.jde.2010.05.014. |
[12] |
C. A. Morales, M. J. Pacifico and E. R. Pujals, Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers,, Ann. of Math., 160 (2004), 375.
doi: 10.4007/annals.2004.160.375. |
[13] |
C. A. Morales, M. J. Pacifico and E. R. Pujals, On $C^1$ robust singular transitive sets for three-dimensional flows,, C. R. Acad. Sci. Paris, 326 (1998), 81.
doi: 10.1016/S0764-4442(97)82717-6. |
[14] |
C. A. Morales, M. J. Pacifico and E. R. Pujals, Singular hyperbolic systems,, Proc. Am. Math. Soc., 127 (1999), 3393.
doi: 10.1090/S0002-9939-99-04936-9. |
[15] |
A. Rovella, The dynamics of perturbations of the contracting Lorenz attractors,, Bol. Soc. Bras. Math., 24 (1993), 233.
doi: 10.1007/BF01237679. |
[16] |
S. Sternberg, On the structure of local homeomorphism of eucliden $n$-spane II,, Am. Journal Math., 80 (1958), 623.
doi: 10.2307/2372774. |
[17] |
T. Vivier, Flots robustement transitifs sur les variétés compactes (French) [Robustly transitive flows on compact manifolds],, Comptes Rendus Acad. Sci. Paris, 337 (2003), 791.
doi: 10.1016/j.crma.2003.10.001. |
show all references
References:
[1] |
V. S. Afraimovich, V. V. Bykov and L. P. Shilnikov, On attracting structurally unstable limit sets of Lorenz attractor type,, Trudy Moskov. Mat. Obshch., 44 (1982), 150.
|
[2] |
V. Araújo and M. J. Pacifico, Three-dimensional Flows, Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series],, 53. Springer, (2010).
doi: 10.1007/978-3-642-11414-4. |
[3] |
R. Bamón, R. Labarca, R. Mańé and M.J. Pacífico, The explosion of singulay cycles,, Inst. Hautes Études Sci. Publ. Math., 78 (1993), 207.
|
[4] |
S. Bautista, The geometric Lorenz attractor is a homoclinic class,, Bol. Mat. (N.S.), 11 (2004), 69.
|
[5] |
C. Bonatti, L. J. Díaz and M. Viana, Dynamics Beyond Uniform Hyperbolicity. A Global Geometric and Probabilistic Perspective, Encyclopaedia of Mathematical Sciences,102, Mathematical Physics III,, Springer-Verlag, (2005).
|
[6] |
D. Carrasco-Olivera, C. A. Morales and B. San Martín, Singular cycles and $C^k$-robust transitive set on manifold with boundary,, Communications in Contemporary Mathematics, 13 (2011), 191.
doi: 10.1142/S0219199711004233. |
[7] |
C. I. Doering, Persistently transitive vector fields on three-dimensional manifolds,, In Procs. on Dynamical Systems and Bifurcations Theory, 160 (1987), 59.
|
[8] |
J. Guckenheimer and R. F. Williams, Structural stability of Lorenz attractors,, Inst. Hautes Études Sci. Publ. Math., 50 (1979), 59.
|
[9] |
M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics,, Vol. 583. Springer-Verlag, (1977).
|
[10] |
M. Milnor, On the concept of attractor,, Comm. Math. Phys., 99 (1985), 177.
doi: 10.1007/BF01212280. |
[11] |
C. A. Morales, Sufficient conditions for a partially hyperbolic attractor to be a homoclinic class,, J. Differential Equations, 249 (2010), 2005.
doi: 10.1016/j.jde.2010.05.014. |
[12] |
C. A. Morales, M. J. Pacifico and E. R. Pujals, Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers,, Ann. of Math., 160 (2004), 375.
doi: 10.4007/annals.2004.160.375. |
[13] |
C. A. Morales, M. J. Pacifico and E. R. Pujals, On $C^1$ robust singular transitive sets for three-dimensional flows,, C. R. Acad. Sci. Paris, 326 (1998), 81.
doi: 10.1016/S0764-4442(97)82717-6. |
[14] |
C. A. Morales, M. J. Pacifico and E. R. Pujals, Singular hyperbolic systems,, Proc. Am. Math. Soc., 127 (1999), 3393.
doi: 10.1090/S0002-9939-99-04936-9. |
[15] |
A. Rovella, The dynamics of perturbations of the contracting Lorenz attractors,, Bol. Soc. Bras. Math., 24 (1993), 233.
doi: 10.1007/BF01237679. |
[16] |
S. Sternberg, On the structure of local homeomorphism of eucliden $n$-spane II,, Am. Journal Math., 80 (1958), 623.
doi: 10.2307/2372774. |
[17] |
T. Vivier, Flots robustement transitifs sur les variétés compactes (French) [Robustly transitive flows on compact manifolds],, Comptes Rendus Acad. Sci. Paris, 337 (2003), 791.
doi: 10.1016/j.crma.2003.10.001. |
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