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Hopf bifurcation at infinity for planar vector fields
Pseudo-orbit shadowing in the $C^1$ topology
1. | Dep. Matemática PUC-Rio, Marquês de São Vicente 225 22453-900, Rio de Janeiro, Brazil, Brazil |
[1] |
Zhiqin Qiao, Deming Zhu, Qiuying Lu. Bifurcation of a heterodimensional cycle with weak inclination flip. Discrete & Continuous Dynamical Systems - B, 2012, 17 (3) : 1009-1025. doi: 10.3934/dcdsb.2012.17.1009 |
[2] |
Samir Adly, Daniel Goeleven, Dumitru Motreanu. Periodic and homoclinic solutions for a class of unilateral problems. Discrete & Continuous Dynamical Systems - A, 1997, 3 (4) : 579-590. doi: 10.3934/dcds.1997.3.579 |
[3] |
Juntao Sun, Jifeng Chu, Zhaosheng Feng. Homoclinic orbits for first order periodic Hamiltonian systems with spectrum point zero. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3807-3824. doi: 10.3934/dcds.2013.33.3807 |
[4] |
Lorenzo J. Díaz, Jorge Rocha. How do hyperbolic homoclinic classes collide at heterodimensional cycles?. Discrete & Continuous Dynamical Systems - A, 2007, 17 (3) : 589-627. doi: 10.3934/dcds.2007.17.589 |
[5] |
Jifeng Chu, Zhaosheng Feng, Ming Li. Periodic shadowing of vector fields. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 3623-3638. doi: 10.3934/dcds.2016.36.3623 |
[6] |
Shaobo Gan, Kazuhiro Sakai, Lan Wen. $C^1$ -stably weakly shadowing homoclinic classes admit dominated splittings. Discrete & Continuous Dynamical Systems - A, 2010, 27 (1) : 205-216. doi: 10.3934/dcds.2010.27.205 |
[7] |
Oksana Koltsova, Lev Lerman. Hamiltonian dynamics near nontransverse homoclinic orbit to saddle-focus equilibrium. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 883-913. doi: 10.3934/dcds.2009.25.883 |
[8] |
Benoît Grébert, Tiphaine Jézéquel, Laurent Thomann. Dynamics of Klein-Gordon on a compact surface near a homoclinic orbit. Discrete & Continuous Dynamical Systems - A, 2014, 34 (9) : 3485-3510. doi: 10.3934/dcds.2014.34.3485 |
[9] |
Shigui Ruan, Junjie Wei, Jianhong Wu. Bifurcation from a homoclinic orbit in partial functional differential equations. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1293-1322. doi: 10.3934/dcds.2003.9.1293 |
[10] |
W.-J. Beyn, Y.-K Zou. Discretizations of dynamical systems with a saddle-node homoclinic orbit. Discrete & Continuous Dynamical Systems - A, 1996, 2 (3) : 351-365. doi: 10.3934/dcds.1996.2.351 |
[11] |
Junxiang Xu. On quasi-periodic perturbations of hyperbolic-type degenerate equilibrium point of a class of planar systems. Discrete & Continuous Dynamical Systems - A, 2013, 33 (6) : 2593-2619. doi: 10.3934/dcds.2013.33.2593 |
[12] |
Katsutoshi Shinohara. On the index problem of $C^1$-generic wild homoclinic classes in dimension three. Discrete & Continuous Dynamical Systems - A, 2011, 31 (3) : 913-940. doi: 10.3934/dcds.2011.31.913 |
[13] |
Piotr Oprocha, Xinxing Wu. On averaged tracing of periodic average pseudo orbits. Discrete & Continuous Dynamical Systems - A, 2017, 37 (9) : 4943-4957. doi: 10.3934/dcds.2017212 |
[14] |
Rafael Ortega. Stability and index of periodic solutions of a nonlinear telegraph equation. Communications on Pure & Applied Analysis, 2005, 4 (4) : 823-837. doi: 10.3934/cpaa.2005.4.823 |
[15] |
Lijun Wei, Xiang Zhang. Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2803-2825. doi: 10.3934/dcds.2016.36.2803 |
[16] |
Anete S. Cavalcanti. An existence proof of a symmetric periodic orbit in the octahedral six-body problem. Discrete & Continuous Dynamical Systems - A, 2017, 37 (4) : 1903-1922. doi: 10.3934/dcds.2017080 |
[17] |
Peter Giesl, James McMichen. Determination of the basin of attraction of a periodic orbit in two dimensions using meshless collocation. Journal of Computational Dynamics, 2016, 3 (2) : 191-210. doi: 10.3934/jcd.2016010 |
[18] |
Tatiane C. Batista, Juliano S. Gonschorowski, Fábio A. Tal. Density of the set of endomorphisms with a maximizing measure supported on a periodic orbit. Discrete & Continuous Dynamical Systems - A, 2015, 35 (8) : 3315-3326. doi: 10.3934/dcds.2015.35.3315 |
[19] |
Wenxiang Sun, Yun Yang. Hyperbolic periodic points for chain hyperbolic homoclinic classes. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 3911-3925. doi: 10.3934/dcds.2016.36.3911 |
[20] |
Flaviano Battelli, Ken Palmer. Transversal periodic-to-periodic homoclinic orbits in singularly perturbed systems. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 367-387. doi: 10.3934/dcdsb.2010.14.367 |
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