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On the reduction of the modified Benjamin-Ono equation to the cubic derivative nonlinear Schrödinger equation
A uniform $C^1$ connecting lemma
1. | School of Mathematic Sciences, Peking University, Beijing, 100871, China |
[1] |
Keonhee Lee, Kazumine Moriyasu, Kazuhiro Sakai. $C^1$-stable shadowing diffeomorphisms. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 683-697. doi: 10.3934/dcds.2008.22.683 |
[2] |
Hermann Köenig, Vitali Milman. Derivative and entropy: the only derivations from $C^1(RR)$ to $C(RR)$. Electronic Research Announcements, 2011, 18: 54-60. doi: 10.3934/era.2011.18.54 |
[3] |
Nikolaz Gourmelon. Generation of homoclinic tangencies by $C^1$-perturbations. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 1-42. doi: 10.3934/dcds.2010.26.1 |
[4] |
Flavio Abdenur, Lorenzo J. Díaz. Pseudo-orbit shadowing in the $C^1$ topology. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 223-245. doi: 10.3934/dcds.2007.17.223 |
[5] |
Christian Bonatti, Sylvain Crovisier and Amie Wilkinson. The centralizer of a $C^1$-generic diffeomorphism is trivial. Electronic Research Announcements, 2008, 15: 33-43. doi: 10.3934/era.2008.15.33 |
[6] |
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 |
[7] |
Yunhua Zhou. The local $C^1$-density of stable ergodicity. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2621-2629. doi: 10.3934/dcds.2013.33.2621 |
[8] |
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 |
[9] |
Mikko Salo. Stability for solutions of wave equations with $C^{1,1}$ coefficients. Inverse Problems and Imaging, 2007, 1 (3) : 537-556. doi: 10.3934/ipi.2007.1.537 |
[10] |
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 |
[11] |
Yun Yang. Horseshoes for $\mathcal{C}^{1+\alpha}$ mappings with hyperbolic measures. Discrete and Continuous Dynamical Systems, 2015, 35 (10) : 5133-5152. doi: 10.3934/dcds.2015.35.5133 |
[12] |
S. Yu. Pilyugin, Kazuhiro Sakai, O. A. Tarakanov. Transversality properties and $C^1$-open sets of diffeomorphisms with weak shadowing. Discrete and Continuous Dynamical Systems, 2006, 16 (4) : 871-882. doi: 10.3934/dcds.2006.16.871 |
[13] |
Christian Bonatti, Sylvain Crovisier, Amie Wilkinson. $C^1$-generic conservative diffeomorphisms have trivial centralizer. Journal of Modern Dynamics, 2008, 2 (2) : 359-373. doi: 10.3934/jmd.2008.2.359 |
[14] |
Rodrigo P. Pacheco, Rafael O. Ruggiero. On C1, β density of metrics without invariant graphs. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 247-261. doi: 10.3934/dcds.2018012 |
[15] |
Juan Wang, Jing Wang, Yongluo Cao, Yun Zhao. Dimensions of $ C^1- $average conformal hyperbolic sets. Discrete and Continuous Dynamical Systems, 2020, 40 (2) : 883-905. doi: 10.3934/dcds.2020065 |
[16] |
Raquel Ribeiro. Hyperbolicity and types of shadowing for $C^1$ generic vector fields. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2963-2982. doi: 10.3934/dcds.2014.34.2963 |
[17] |
Christian Bonatti, Sylvain Crovisier, Katsutoshi Shinohara. The $C^{1+\alpha }$ hypothesis in Pesin Theory revisited. Journal of Modern Dynamics, 2013, 7 (4) : 605-618. doi: 10.3934/jmd.2013.7.605 |
[18] |
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 |
[19] |
Andrey Gogolev, Misha Guysinsky. $C^1$-differentiable conjugacy of Anosov diffeomorphisms on three dimensional torus. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 183-200. doi: 10.3934/dcds.2008.22.183 |
[20] |
Matteo Cozzi. On the variation of the fractional mean curvature under the effect of $C^{1, \alpha}$ perturbations. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 5769-5786. doi: 10.3934/dcds.2015.35.5769 |
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