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On the intersection of sectional-hyperbolic sets
1. | Universidad Nacional de Colombia, Depto. de Matemáticas, Facultad de Ciencias, Bogota, Colombia |
2. | Instituto de Matemática, Universidade Federal do Rio de Janeiro,, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil |
References:
[1] |
V. S. Afraĭmovič, V. V. Bykov and L. P. Sil'nikov, The origin and structure of the Lorenz attractor,, Dokl. Akad. Nauk SSSR, 234 (1977), 336.
|
[2] |
V. Araújo and M. J. Pacifico, Three-Dimensional Flows,, With a foreword by Marcelo Viana, (2010).
doi: 10.1007/978-3-642-11414-4. |
[3] |
V. Araujo and L. Salgado, Infinitesimal Lyapunov functions for singular flows,, Math. Z., 275 (2013), 863.
doi: 10.1007/s00209-013-1163-8. |
[4] |
A. Arbieto and C. A. Morales, A dichotomy for higher-dimensional flows,, Proc. Amer. Math. Soc., 141 (2013), 2817.
doi: 10.1090/S0002-9939-2013-11536-4. |
[5] |
R. Bamon, R. Labarca, R. Mañé and M. J. Pacifico, The explosion of singular cycles,, Inst. Hautes Études Sci. Publ. Math., 78 (1993), 207.
|
[6] |
S. Bautista, The geometric Lorenz attractor is a homoclinic class,, Bol. Mat. (N.S.), 11 (2004), 69.
|
[7] |
S. Bautista and C. A. Morales, Lectures on Sectional-Anosov Flows,, preprint, (). Google Scholar |
[8] |
S. Bautista, C. A. Morales and M. J. Pacifico, On the intersection of homoclinic classes on singular-hyperbolic sets,, Discrete Contin. Dyn. Syst., 19 (2007), 761.
doi: 10.3934/dcds.2007.19.761. |
[9] |
C. Bonatti, A. Pumariño and M. Viana, Lorenz attractors with arbitrary expanding dimension,, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), 883.
doi: 10.1016/S0764-4442(97)80131-0. |
[10] |
C. Diminnie, S. Gahler and A. White, $2$-inner product spaces,, Collection of articles dedicated to Stanisław Gołąb on his 70th birthday, 6 (1973), 525.
|
[11] |
S. Gan and L. Wen, Nonsingular star flows satisfy Axiom A and the no-cycle condition,, Invent. Math., 164 (2006), 279.
doi: 10.1007/s00222-005-0479-3. |
[12] |
S. Gähler, Lineare 2-normierte Räume,, Math. Nachr., 28 (1964), 1.
doi: 10.1002/mana.19640280102. |
[13] |
J. Guckenheimer and R. Williams, Structural stability of Lorenz attractors,, Inst. Hautes Études Sci. Publ. Math., 50 (1979), 59.
|
[14] |
M. Hirsch, C. Pugh and M. Shub, Invariant Manifolds,, Lecture Notes in Math., (1977).
|
[15] |
A. Kawaguchi, On areal spaces. I. Metric tensors in $n$-dimensional spaces based on the notion of two-dimensional area,, Tensor N.S., 1 (1950), 14.
|
[16] |
R. Labarca and M. J. Pacifico, Stability of singularity horseshoes,, Topology, 25 (1986), 337.
doi: 10.1016/0040-9383(86)90048-0. |
[17] |
A. M. López, Sectional Hyperbolic Sets in Higher Dimensions,, Tese de Doutorado, (2015). Google Scholar |
[18] |
A. M. López and H. Sánchez, Sectional Anosov flows: Existence of Venice masks with two singularities,, , (). Google Scholar |
[19] |
R. Metzger and C. A. Morales, Sectional-hyperbolic systems,, Ergodic Theory Dynam. Systems, 28 (2008), 1587.
doi: 10.1017/S0143385707000995. |
[20] |
C. A. Morales and M. J. Pacifico, A dichotomy for three-dimensional vector fields,, Ergodic Theory Dynam. Systems, 23 (2003), 1575.
doi: 10.1017/S0143385702001621. |
[21] |
C. A. Morales and M. J. Pacifico, Sufficient conditions for robustness of attractors,, Pacific J. Math., 216 (2004), 327.
doi: 10.2140/pjm.2004.216.327. |
[22] |
C. A. Morales and M. J. Pacifico, A spectral decomposition for singular-hyperbolic sets,, Pacific J. Math., 229 (2007), 223.
doi: 10.2140/pjm.2007.229.223. |
[23] |
C. A. Morales and M. Vilches, On 2-Riemannian manifolds,, SUT J. Math., 46 (2010), 119.
|
[24] |
S. Newhouse, On simple arcs between structurally stable flows,, in Dynamical Systems-Warwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, (1974), 209.
|
[25] |
Y. Shi, S. Gan and L. Wen, On the singular-hyperbolicity of star flows,, J. Mod. Dyn., 8 (2014), 191.
doi: 10.3934/jmd.2014.8.191. |
[26] |
S. Zhu, S. Gan and L. Wen, Indices of singularities of robustly transitive sets,, Discrete Contin. Dyn. Syst., 21 (2008), 945.
doi: 10.3934/dcds.2008.21.945. |
show all references
References:
[1] |
V. S. Afraĭmovič, V. V. Bykov and L. P. Sil'nikov, The origin and structure of the Lorenz attractor,, Dokl. Akad. Nauk SSSR, 234 (1977), 336.
|
[2] |
V. Araújo and M. J. Pacifico, Three-Dimensional Flows,, With a foreword by Marcelo Viana, (2010).
doi: 10.1007/978-3-642-11414-4. |
[3] |
V. Araujo and L. Salgado, Infinitesimal Lyapunov functions for singular flows,, Math. Z., 275 (2013), 863.
doi: 10.1007/s00209-013-1163-8. |
[4] |
A. Arbieto and C. A. Morales, A dichotomy for higher-dimensional flows,, Proc. Amer. Math. Soc., 141 (2013), 2817.
doi: 10.1090/S0002-9939-2013-11536-4. |
[5] |
R. Bamon, R. Labarca, R. Mañé and M. J. Pacifico, The explosion of singular cycles,, Inst. Hautes Études Sci. Publ. Math., 78 (1993), 207.
|
[6] |
S. Bautista, The geometric Lorenz attractor is a homoclinic class,, Bol. Mat. (N.S.), 11 (2004), 69.
|
[7] |
S. Bautista and C. A. Morales, Lectures on Sectional-Anosov Flows,, preprint, (). Google Scholar |
[8] |
S. Bautista, C. A. Morales and M. J. Pacifico, On the intersection of homoclinic classes on singular-hyperbolic sets,, Discrete Contin. Dyn. Syst., 19 (2007), 761.
doi: 10.3934/dcds.2007.19.761. |
[9] |
C. Bonatti, A. Pumariño and M. Viana, Lorenz attractors with arbitrary expanding dimension,, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), 883.
doi: 10.1016/S0764-4442(97)80131-0. |
[10] |
C. Diminnie, S. Gahler and A. White, $2$-inner product spaces,, Collection of articles dedicated to Stanisław Gołąb on his 70th birthday, 6 (1973), 525.
|
[11] |
S. Gan and L. Wen, Nonsingular star flows satisfy Axiom A and the no-cycle condition,, Invent. Math., 164 (2006), 279.
doi: 10.1007/s00222-005-0479-3. |
[12] |
S. Gähler, Lineare 2-normierte Räume,, Math. Nachr., 28 (1964), 1.
doi: 10.1002/mana.19640280102. |
[13] |
J. Guckenheimer and R. Williams, Structural stability of Lorenz attractors,, Inst. Hautes Études Sci. Publ. Math., 50 (1979), 59.
|
[14] |
M. Hirsch, C. Pugh and M. Shub, Invariant Manifolds,, Lecture Notes in Math., (1977).
|
[15] |
A. Kawaguchi, On areal spaces. I. Metric tensors in $n$-dimensional spaces based on the notion of two-dimensional area,, Tensor N.S., 1 (1950), 14.
|
[16] |
R. Labarca and M. J. Pacifico, Stability of singularity horseshoes,, Topology, 25 (1986), 337.
doi: 10.1016/0040-9383(86)90048-0. |
[17] |
A. M. López, Sectional Hyperbolic Sets in Higher Dimensions,, Tese de Doutorado, (2015). Google Scholar |
[18] |
A. M. López and H. Sánchez, Sectional Anosov flows: Existence of Venice masks with two singularities,, , (). Google Scholar |
[19] |
R. Metzger and C. A. Morales, Sectional-hyperbolic systems,, Ergodic Theory Dynam. Systems, 28 (2008), 1587.
doi: 10.1017/S0143385707000995. |
[20] |
C. A. Morales and M. J. Pacifico, A dichotomy for three-dimensional vector fields,, Ergodic Theory Dynam. Systems, 23 (2003), 1575.
doi: 10.1017/S0143385702001621. |
[21] |
C. A. Morales and M. J. Pacifico, Sufficient conditions for robustness of attractors,, Pacific J. Math., 216 (2004), 327.
doi: 10.2140/pjm.2004.216.327. |
[22] |
C. A. Morales and M. J. Pacifico, A spectral decomposition for singular-hyperbolic sets,, Pacific J. Math., 229 (2007), 223.
doi: 10.2140/pjm.2007.229.223. |
[23] |
C. A. Morales and M. Vilches, On 2-Riemannian manifolds,, SUT J. Math., 46 (2010), 119.
|
[24] |
S. Newhouse, On simple arcs between structurally stable flows,, in Dynamical Systems-Warwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, (1974), 209.
|
[25] |
Y. Shi, S. Gan and L. Wen, On the singular-hyperbolicity of star flows,, J. Mod. Dyn., 8 (2014), 191.
doi: 10.3934/jmd.2014.8.191. |
[26] |
S. Zhu, S. Gan and L. Wen, Indices of singularities of robustly transitive sets,, Discrete Contin. Dyn. Syst., 21 (2008), 945.
doi: 10.3934/dcds.2008.21.945. |
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