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Robustly expansive homoclinic classes are generically hyperbolic
1. | Facultad de Ciencias, Iguá 4225 y Mataojo, Universidad de la República, Montevideo |
2. | Facultad deIngeniería, Herrera y Reissig 565, Universidad de la República, Montevideo, Uruguay |
[1] |
Christian Bonatti, Shaobo Gan, Dawei Yang. On the hyperbolicity of homoclinic classes. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1143-1162. doi: 10.3934/dcds.2009.25.1143 |
[2] |
Eleonora Catsigeras, Xueting Tian. Dominated splitting, partial hyperbolicity and positive entropy. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4739-4759. doi: 10.3934/dcds.2016006 |
[3] |
Keonhee Lee, Manseob Lee. Hyperbolicity of $C^1$-stably expansive homoclinic classes. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 1133-1145. doi: 10.3934/dcds.2010.27.1133 |
[4] |
Shaobo Gan, Kazuhiro Sakai, Lan Wen. $C^1$ -stably weakly shadowing homoclinic classes admit dominated splittings. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 205-216. doi: 10.3934/dcds.2010.27.205 |
[5] |
Dante Carrasco-Olivera, Bernardo San Martín. Robust attractors without dominated splitting on manifolds with boundary. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4555-4563. doi: 10.3934/dcds.2014.34.4555 |
[6] |
Wenxiang Sun, Xueting Tian. Dominated splitting and Pesin's entropy formula. Discrete and Continuous Dynamical Systems, 2012, 32 (4) : 1421-1434. doi: 10.3934/dcds.2012.32.1421 |
[7] |
Xiao Wen. Structurally stable homoclinic classes. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1693-1707. doi: 10.3934/dcds.2016.36.1693 |
[8] |
Xinsheng Wang, Lin Wang, Yujun Zhu. Formula of entropy along unstable foliations for $C^1$ diffeomorphisms with dominated splitting. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 2125-2140. doi: 10.3934/dcds.2018087 |
[9] |
Pedro Duarte, Silvius Klein. Topological obstructions to dominated splitting for ergodic translations on the higher dimensional torus. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 5379-5387. doi: 10.3934/dcds.2018237 |
[10] |
S. Bautista, C. Morales, M. J. Pacifico. On the intersection of homoclinic classes on singular-hyperbolic sets. Discrete and Continuous Dynamical Systems, 2007, 19 (4) : 761-775. doi: 10.3934/dcds.2007.19.761 |
[11] |
Wenxiang Sun, Yun Yang. Hyperbolic periodic points for chain hyperbolic homoclinic classes. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3911-3925. doi: 10.3934/dcds.2016.36.3911 |
[12] |
Martín Sambarino, José L. Vieitez. On $C^1$-persistently expansive homoclinic classes. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 465-481. doi: 10.3934/dcds.2006.14.465 |
[13] |
Enrique R. Pujals. On the density of hyperbolicity and homoclinic bifurcations for 3D-diffeomorphisms in attracting regions. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 179-226. doi: 10.3934/dcds.2006.16.179 |
[14] |
Enrique R. Pujals. Density of hyperbolicity and homoclinic bifurcations for attracting topologically hyperbolic sets. Discrete and Continuous Dynamical Systems, 2008, 20 (2) : 335-405. doi: 10.3934/dcds.2008.20.335 |
[15] |
Lorenzo J. Díaz, Jorge Rocha. How do hyperbolic homoclinic classes collide at heterodimensional cycles?. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 589-627. doi: 10.3934/dcds.2007.17.589 |
[16] |
Christian Bonatti, Lorenzo J. Díaz, Todd Fisher. Super-exponential growth of the number of periodic orbits inside homoclinic classes. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 589-604. doi: 10.3934/dcds.2008.20.589 |
[17] |
Katsutoshi Shinohara. On the index problem of $C^1$-generic wild homoclinic classes in dimension three. Discrete and Continuous Dynamical Systems, 2011, 31 (3) : 913-940. doi: 10.3934/dcds.2011.31.913 |
[18] |
Welington Cordeiro, Manfred Denker, Xuan Zhang. On specification and measure expansiveness. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 1941-1957. doi: 10.3934/dcds.2017082 |
[19] |
Welington Cordeiro, Manfred Denker, Xuan Zhang. Corrigendum to: On specification and measure expansiveness. Discrete and Continuous Dynamical Systems, 2018, 38 (7) : 3705-3706. doi: 10.3934/dcds.2018160 |
[20] |
Karsten Matthies. Exponentially small splitting of homoclinic orbits of parabolic differential equations under periodic forcing. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 585-602. doi: 10.3934/dcds.2003.9.585 |
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