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Generation of homoclinic tangencies by $C^1$-perturbations
1. | Université Bordeaux 1, 351, cours de la Libération, F 33405 TALENCE cedex, France |
[1] |
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 |
[2] |
Rui Dilão, András Volford. Excitability in a model with a saddle-node homoclinic bifurcation. Discrete and Continuous Dynamical Systems - B, 2004, 4 (2) : 419-434. doi: 10.3934/dcdsb.2004.4.419 |
[3] |
Pablo Aguirre, Bernd Krauskopf, Hinke M. Osinga. Global invariant manifolds near a Shilnikov homoclinic bifurcation. Journal of Computational Dynamics, 2014, 1 (1) : 1-38. doi: 10.3934/jcd.2014.1.1 |
[4] |
S. Secchi, C. A. Stuart. Global bifurcation of homoclinic solutions of Hamiltonian systems. Discrete and Continuous Dynamical Systems, 2003, 9 (6) : 1493-1518. doi: 10.3934/dcds.2003.9.1493 |
[5] |
Ying Lv, Yan-Fang Xue, Chun-Lei Tang. Homoclinic orbits for a class of asymptotically quadratic Hamiltonian systems. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2855-2878. doi: 10.3934/cpaa.2019128 |
[6] |
Samir Adly, Daniel Goeleven, Dumitru Motreanu. Periodic and homoclinic solutions for a class of unilateral problems. Discrete and Continuous Dynamical Systems, 1997, 3 (4) : 579-590. doi: 10.3934/dcds.1997.3.579 |
[7] |
Flaviano Battelli. Saddle-node bifurcation of homoclinic orbits in singular systems. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 203-218. doi: 10.3934/dcds.2001.7.203 |
[8] |
Shigui Ruan, Junjie Wei, Jianhong Wu. Bifurcation from a homoclinic orbit in partial functional differential equations. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1293-1322. doi: 10.3934/dcds.2003.9.1293 |
[9] |
Andrus Giraldo, Bernd Krauskopf, Hinke M. Osinga. Computing connecting orbits to infinity associated with a homoclinic flip bifurcation. Journal of Computational Dynamics, 2020, 7 (2) : 489-510. doi: 10.3934/jcd.2020020 |
[10] |
Flaviano Battelli, Claudio Lazzari. On the bifurcation from critical homoclinic orbits in n-dimensional maps. Discrete and Continuous Dynamical Systems, 1997, 3 (2) : 289-303. doi: 10.3934/dcds.1997.3.289 |
[11] |
Addolorata Salvatore. Multiple homoclinic orbits for a class of second order perturbed Hamiltonian systems. Conference Publications, 2003, 2003 (Special) : 778-787. doi: 10.3934/proc.2003.2003.778 |
[12] |
Jun Wang, Junxiang Xu, Fubao Zhang. Homoclinic orbits for a class of Hamiltonian systems with superquadratic or asymptotically quadratic potentials. Communications on Pure and Applied Analysis, 2011, 10 (1) : 269-286. doi: 10.3934/cpaa.2011.10.269 |
[13] |
Tiantian Wu, Xiao-Song Yang. A new class of 3-dimensional piecewise affine systems with homoclinic orbits. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 5119-5129. doi: 10.3934/dcds.2016022 |
[14] |
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 |
[15] |
Amadeu Delshams, Pere Gutiérrez. Exponentially small splitting for whiskered tori in Hamiltonian systems: continuation of transverse homoclinic orbits. Discrete and Continuous Dynamical Systems, 2004, 11 (4) : 757-783. doi: 10.3934/dcds.2004.11.757 |
[16] |
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 |
[17] |
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 |
[18] |
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 |
[19] |
Xianjun Wang, Huaguang Gu, Bo Lu. Big homoclinic orbit bifurcation underlying post-inhibitory rebound spike and a novel threshold curve of a neuron. Electronic Research Archive, 2021, 29 (5) : 2987-3015. doi: 10.3934/era.2021023 |
[20] |
Xiao Wen. Structurally stable homoclinic classes. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1693-1707. doi: 10.3934/dcds.2016.36.1693 |
2020 Impact Factor: 1.392
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