November  2014, 34(11): 4555-4563. doi: 10.3934/dcds.2014.34.4555

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

Received  August 2013 Revised  February 2014 Published  May 2014

In this paper we prove that there exists a positive integer $k$ with the following property: Every compact $3$-manifold with boundary carries a $C^\infty$ vector field exhibiting a $C^k$-robust attractor without dominated splitting in a robust sense.
Citation: Dante Carrasco-Olivera, Bernardo San Martín. Robust attractors without dominated splitting on manifolds with boundary. Discrete & Continuous Dynamical Systems, 2014, 34 (11) : 4555-4563. doi: 10.3934/dcds.2014.34.4555
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show all references

References:
[1]

Trudy Moskov. Mat. Obshch., 44 (1982), 150-212 (Russian).  Google Scholar

[2]

53. Springer, Heidelberg, 2010. doi: 10.1007/978-3-642-11414-4.  Google Scholar

[3]

Inst. Hautes Études Sci. Publ. Math., 78 (1993), 207-232.  Google Scholar

[4]

Bol. Mat. (N.S.), 11 (2004), 69-78.  Google Scholar

[5]

Springer-Verlag, Berlin, 2005.  Google Scholar

[6]

Communications in Contemporary Mathematics, 13 (2011), 191-211. doi: 10.1142/S0219199711004233.  Google Scholar

[7]

In Procs. on Dynamical Systems and Bifurcations Theory, 160 (1987), 59-89.  Google Scholar

[8]

Inst. Hautes Études Sci. Publ. Math., 50 (1979), 59-72.  Google Scholar

[9]

Vol. 583. Springer-Verlag, Berlin-New York, 1977  Google Scholar

[10]

Comm. Math. Phys., 99 (1985), 177-195. doi: 10.1007/BF01212280.  Google Scholar

[11]

J. Differential Equations, 249 (2010), 2005-2020. doi: 10.1016/j.jde.2010.05.014.  Google Scholar

[12]

Ann. of Math., 160 (2004), 375-432. doi: 10.4007/annals.2004.160.375.  Google Scholar

[13]

C. R. Acad. Sci. Paris, 326 (1998), 81-86. doi: 10.1016/S0764-4442(97)82717-6.  Google Scholar

[14]

Proc. Am. Math. Soc., 127 (1999), 3393-3401. doi: 10.1090/S0002-9939-99-04936-9.  Google Scholar

[15]

Bol. Soc. Bras. Math., 24 (1993), 233-259. doi: 10.1007/BF01237679.  Google Scholar

[16]

Am. Journal Math., 80 (1958), 623-631. doi: 10.2307/2372774.  Google Scholar

[17]

Comptes Rendus Acad. Sci. Paris, 337 (2003), 791-796. doi: 10.1016/j.crma.2003.10.001.  Google Scholar

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