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Persistence of lower dimensional elliptic invariant tori for a class of nearly integrable reversible systems
1. | Faculty of mathematics and physics, Huaiyin Institute of Technology, Huaian, Jiangsu 223003, China |
2. | Department of Mathematics, Southeast University, Nanjing 210096 |
[1] |
Xiaocai Wang. Non-floquet invariant tori in reversible systems. Discrete and Continuous Dynamical Systems, 2018, 38 (7) : 3439-3457. doi: 10.3934/dcds.2018147 |
[2] |
Shengqing Hu. Persistence of invariant tori for almost periodically forced reversible systems. Discrete and Continuous Dynamical Systems, 2020, 40 (7) : 4497-4518. doi: 10.3934/dcds.2020188 |
[3] |
Xiaocai Wang, Junxiang Xu, Dongfeng Zhang. A KAM theorem for the elliptic lower dimensional tori with one normal frequency in reversible systems. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 2141-2160. doi: 10.3934/dcds.2017092 |
[4] |
Shengqing Hu, Bin Liu. Degenerate lower dimensional invariant tori in reversible system. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 3735-3763. doi: 10.3934/dcds.2018162 |
[5] |
Xiaocai Wang, Junxiang Xu. Gevrey-smoothness of invariant tori for analytic reversible systems under Rüssmann's non-degeneracy condition. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 701-718. doi: 10.3934/dcds.2009.25.701 |
[6] |
Helmut Rüssmann. KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character. Discrete and Continuous Dynamical Systems - S, 2010, 3 (4) : 683-718. doi: 10.3934/dcdss.2010.3.683 |
[7] |
Xiaocai Wang, Junxiang Xu, Dongfeng Zhang. On the persistence of lower-dimensional elliptic tori with prescribed frequencies in reversible systems. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1677-1692. doi: 10.3934/dcds.2016.36.1677 |
[8] |
Fuzhong Cong, Yong Li. Invariant hyperbolic tori for Hamiltonian systems with degeneracy. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 371-382. doi: 10.3934/dcds.1997.3.371 |
[9] |
C. Chandre. Renormalization for cubic frequency invariant tori in Hamiltonian systems with two degrees of freedom. Discrete and Continuous Dynamical Systems - B, 2002, 2 (3) : 457-465. doi: 10.3934/dcdsb.2002.2.457 |
[10] |
Xiaocai Wang, Xiaofei Cao, Xuqing Liu. On the persistence of lower-dimensional tori in reversible systems with high dimensional degenerate equilibrium under small perturbations. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022004 |
[11] |
Luca Biasco, Luigi Chierchia. On the measure of KAM tori in two degrees of freedom. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 6635-6648. doi: 10.3934/dcds.2020134 |
[12] |
Dongfeng Yan. KAM Tori for generalized Benjamin-Ono equation. Communications on Pure and Applied Analysis, 2015, 14 (3) : 941-957. doi: 10.3934/cpaa.2015.14.941 |
[13] |
Guanghua Shi, Dongfeng Yan. KAM tori for quintic nonlinear schrödinger equations with given potential. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2421-2439. doi: 10.3934/dcds.2020120 |
[14] |
Mikhail B. Sevryuk. Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 569-595. doi: 10.3934/dcds.2007.18.569 |
[15] |
Xuemei Li, Zaijiu Shang. On the existence of invariant tori in non-conservative dynamical systems with degeneracy and finite differentiability. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 4225-4257. doi: 10.3934/dcds.2019171 |
[16] |
Paul H. Rabinowitz. On a class of reversible elliptic systems. Networks and Heterogeneous Media, 2012, 7 (4) : 927-939. doi: 10.3934/nhm.2012.7.927 |
[17] |
Hsuan-Wen Su. Finding invariant tori with Poincare's map. Communications on Pure and Applied Analysis, 2008, 7 (2) : 433-443. doi: 10.3934/cpaa.2008.7.433 |
[18] |
Ugo Locatelli, Antonio Giorgilli. Invariant tori in the Sun--Jupiter--Saturn system. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 377-398. doi: 10.3934/dcdsb.2007.7.377 |
[19] |
Hans Koch. On the renormalization of Hamiltonian flows, and critical invariant tori. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 633-646. doi: 10.3934/dcds.2002.8.633 |
[20] |
Peng Huang. Existence of invariant curves for degenerate almost periodic reversible mappings. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022074 |
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