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Rigorous high-dimensional shadowing using containment: The general case
Heteroclinic orbits and rotation sets for twist maps
1. | Department of Mathematics, Instituto Tecnológico Autónomo de México, Río Hondo # 1., Tizapán San Angel, México DF 01000, Mexico |
[1] |
Tifei Qian, Zhihong Xia. Heteroclinic orbits and chaotic invariant sets for monotone twist maps. Discrete and Continuous Dynamical Systems, 2003, 9 (1) : 69-95. doi: 10.3934/dcds.2003.9.69 |
[2] |
Qiudong Wang. The diffusion time of the connecting orbit around rotation number zero for the monotone twist maps. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 255-274. doi: 10.3934/dcds.2000.6.255 |
[3] |
Sergey V. Bolotin. Shadowing chains of collision orbits. Discrete and Continuous Dynamical Systems, 2006, 14 (2) : 235-260. doi: 10.3934/dcds.2006.14.235 |
[4] |
Salvador Addas-Zanata. Stability for the vertical rotation interval of twist mappings. Discrete and Continuous Dynamical Systems, 2006, 14 (4) : 631-642. doi: 10.3934/dcds.2006.14.631 |
[5] |
John Erik Fornæss. Periodic points of holomorphic twist maps. Discrete and Continuous Dynamical Systems, 2005, 13 (4) : 1047-1056. doi: 10.3934/dcds.2005.13.1047 |
[6] |
Zhihong Xia, Peizheng Yu. A fixed point theorem for twist maps. Discrete and Continuous Dynamical Systems, 2022, 42 (8) : 4051-4059. doi: 10.3934/dcds.2022045 |
[7] |
Daniel Wilczak, Piotr Zgliczyński. Topological method for symmetric periodic orbits for maps with a reversing symmetry. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 629-652. doi: 10.3934/dcds.2007.17.629 |
[8] |
Christopher Cleveland. Rotation sets for unimodal maps of the interval. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 617-632. doi: 10.3934/dcds.2003.9.617 |
[9] |
Christopher K. R. T. Jones, Siu-Kei Tin. Generalized exchange lemmas and orbits heteroclinic to invariant manifolds. Discrete and Continuous Dynamical Systems - S, 2009, 2 (4) : 967-1023. doi: 10.3934/dcdss.2009.2.967 |
[10] |
Fei Liu, Jaume Llibre, Xiang Zhang. Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1097-1111. doi: 10.3934/dcds.2011.29.1097 |
[11] |
Thorsten Hüls, Yongkui Zou. On computing heteroclinic trajectories of non-autonomous maps. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 79-99. doi: 10.3934/dcdsb.2012.17.79 |
[12] |
Katja Polotzek, Kathrin Padberg-Gehle, Tobias Jäger. Set-oriented numerical computation of rotation sets. Journal of Computational Dynamics, 2017, 4 (1&2) : 119-141. doi: 10.3934/jcd.2017004 |
[13] |
Kazuyuki Yagasaki. Application of the subharmonic Melnikov method to piecewise-smooth systems. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 2189-2209. doi: 10.3934/dcds.2013.33.2189 |
[14] |
Daniel Wilczak. Abundance of heteroclinic and homoclinic orbits for the hyperchaotic Rössler system. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 1039-1055. doi: 10.3934/dcdsb.2009.11.1039 |
[15] |
Artem Dudko. Computability of the Julia set. Nonrecurrent critical orbits. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2751-2778. doi: 10.3934/dcds.2014.34.2751 |
[16] |
Kazuyuki Yagasaki. Higher-order Melnikov method and chaos for two-degree-of-freedom Hamiltonian systems with saddle-centers. Discrete and Continuous Dynamical Systems, 2011, 29 (1) : 387-402. doi: 10.3934/dcds.2011.29.387 |
[17] |
Miguel Mendes. A note on the coding of orbits in certain discontinuous maps. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 369-382. doi: 10.3934/dcds.2010.27.369 |
[18] |
Chris Bernhardt. Vertex maps for trees: Algebra and periods of periodic orbits. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 399-408. doi: 10.3934/dcds.2006.14.399 |
[19] |
Yakov Krasnov, Alexander Kononovich, Grigory Osharovich. On a structure of the fixed point set of homogeneous maps. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 1017-1027. doi: 10.3934/dcdss.2013.6.1017 |
[20] |
Yiming Ding. Renormalization and $\alpha$-limit set for expanding Lorenz maps. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 979-999. doi: 10.3934/dcds.2011.29.979 |
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