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Polynomial differential equations with small coefficients
On the hyperbolicity of homoclinic classes
1. | Institut de Mathématiques de Bourgogne, Université de Bourgogne, Dijon 21004, France |
2. | School of Mathematical Science, Peking University, Beijing 100871 |
3. | School of Mathematical Sciences, Peking University, Beijing 100871, China |
[1] |
Amadeu Delshams, Marian Gidea, Pablo Roldán. Transition map and shadowing lemma for normally hyperbolic invariant manifolds. Discrete and Continuous Dynamical Systems, 2013, 33 (3) : 1089-1112. doi: 10.3934/dcds.2013.33.1089 |
[2] |
Shaobo Gan. A generalized shadowing lemma. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 627-632. doi: 10.3934/dcds.2002.8.627 |
[3] |
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 |
[4] |
Xiao Wen, Lan Wen. No-shadowing for singular hyperbolic sets with a singularity. Discrete and Continuous Dynamical Systems, 2020, 40 (10) : 6043-6059. doi: 10.3934/dcds.2020258 |
[5] |
Zhiping Li, Yunhua Zhou. Quasi-shadowing for partially hyperbolic flows. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2089-2103. doi: 10.3934/dcds.2020107 |
[6] |
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 |
[7] |
Jacky Cresson. The transfer lemma for Graff tori and Arnold diffusion time. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 787-800. doi: 10.3934/dcds.2001.7.787 |
[8] |
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 |
[9] |
Martín Sambarino, José L. Vieitez. Robustly expansive homoclinic classes are generically hyperbolic. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1325-1333. doi: 10.3934/dcds.2009.24.1325 |
[10] |
Yahui Niu. A Hopf type lemma and the symmetry of solutions for a class of Kirchhoff equations. Communications on Pure and Applied Analysis, 2021, 20 (4) : 1431-1445. doi: 10.3934/cpaa.2021027 |
[11] |
Rafael O. Ruggiero. Shadowing of geodesics, weak stability of the geodesic flow and global hyperbolic geometry. Discrete and Continuous Dynamical Systems, 2006, 14 (2) : 365-383. doi: 10.3934/dcds.2006.14.365 |
[12] |
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 |
[13] |
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 |
[14] |
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 |
[15] |
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 |
[16] |
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 |
[17] |
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 |
[18] |
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 |
[19] |
Graziano Crasta, Philippe G. LeFloch. Existence result for a class of nonconservative and nonstrictly hyperbolic systems. Communications on Pure and Applied Analysis, 2002, 1 (4) : 513-530. doi: 10.3934/cpaa.2002.1.513 |
[20] |
Todor Gramchev, Nicola Orrú. Cauchy problem for a class of nondiagonalizable hyperbolic systems. Conference Publications, 2011, 2011 (Special) : 533-542. doi: 10.3934/proc.2011.2011.533 |
2020 Impact Factor: 1.392
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