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Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method
1. | Institute of Energy Problems of Chemical Physics, The Russia Academy of Sciences, Leninskiĭ prospect 38, Bldg. 2, Moscow 119334, Russian Federation |
[1] |
Àlex Haro, Rafael de la Llave. A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: Numerical algorithms. Discrete and Continuous Dynamical Systems - B, 2006, 6 (6) : 1261-1300. doi: 10.3934/dcdsb.2006.6.1261 |
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Peng Huang, Xiong Li, Bin Liu. Invariant curves of smooth quasi-periodic mappings. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 131-154. doi: 10.3934/dcds.2018006 |
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Qihuai Liu, Dingbian Qian, Zhiguo Wang. Quasi-periodic solutions of the Lotka-Volterra competition systems with quasi-periodic perturbations. Discrete and Continuous Dynamical Systems - B, 2012, 17 (5) : 1537-1550. doi: 10.3934/dcdsb.2012.17.1537 |
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Xin Zhang, Shuangling Yang. Complex dynamics in a quasi-periodic plasma perturbations model. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4013-4043. doi: 10.3934/dcdsb.2020272 |
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Ugo Locatelli, Letizia Stefanelli. Quasi-periodic motions in a special class of dynamical equations with dissipative effects: A pair of detection methods. Discrete and Continuous Dynamical Systems - B, 2015, 20 (4) : 1155-1187. doi: 10.3934/dcdsb.2015.20.1155 |
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Zhichao Ma, Junxiang Xu. A KAM theorem for quasi-periodic non-twist mappings and its application. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022013 |
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Claudia Valls. On the quasi-periodic solutions of generalized Kaup systems. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 467-482. doi: 10.3934/dcds.2015.35.467 |
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Jean Bourgain. On quasi-periodic lattice Schrödinger operators. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 75-88. doi: 10.3934/dcds.2004.10.75 |
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Bochao Chen, Yixian Gao. Quasi-periodic travelling waves for beam equations with damping on 3-dimensional rectangular tori. Discrete and Continuous Dynamical Systems - B, 2022, 27 (2) : 921-944. doi: 10.3934/dcdsb.2021075 |
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Yanling Shi, Junxiang Xu, Xindong Xu. Quasi-periodic solutions of generalized Boussinesq equation with quasi-periodic forcing. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2501-2519. doi: 10.3934/dcdsb.2017104 |
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Lei Jiao, Yiqian Wang. The construction of quasi-periodic solutions of quasi-periodic forced Schrödinger equation. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1585-1606. doi: 10.3934/cpaa.2009.8.1585 |
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Junxiang Xu. On quasi-periodic perturbations of hyperbolic-type degenerate equilibrium point of a class of planar systems. Discrete and Continuous Dynamical Systems, 2013, 33 (6) : 2593-2619. doi: 10.3934/dcds.2013.33.2593 |
[13] |
Ernest Fontich, Rafael de la Llave, Yannick Sire. A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems. Electronic Research Announcements, 2009, 16: 9-22. doi: 10.3934/era.2009.16.9 |
[14] |
Alessandro Fonda, Antonio J. Ureña. Periodic, subharmonic, and quasi-periodic oscillations under the action of a central force. Discrete and Continuous Dynamical Systems, 2011, 29 (1) : 169-192. doi: 10.3934/dcds.2011.29.169 |
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Xavier Blanc, Claude Le Bris. Improving on computation of homogenized coefficients in the periodic and quasi-periodic settings. Networks and Heterogeneous Media, 2010, 5 (1) : 1-29. doi: 10.3934/nhm.2010.5.1 |
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Gerard Gómez, Josep–Maria Mondelo, Carles Simó. A collocation method for the numerical Fourier analysis of quasi-periodic functions. I: Numerical tests and examples. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 41-74. doi: 10.3934/dcdsb.2010.14.41 |
[17] |
Gerard Gómez, Josep–Maria Mondelo, Carles Simó. A collocation method for the numerical Fourier analysis of quasi-periodic functions. II: Analytical error estimates. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 75-109. doi: 10.3934/dcdsb.2010.14.75 |
[18] |
Yanling Shi, Junxiang Xu. Quasi-periodic solutions for a class of beam equation system. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 31-53. doi: 10.3934/dcdsb.2019171 |
[19] |
Jinhao Liang. Positive Lyapunov exponent for a class of quasi-periodic cocycles. Discrete and Continuous Dynamical Systems, 2020, 40 (3) : 1361-1387. doi: 10.3934/dcds.2020080 |
[20] |
Russell Johnson, Francesca Mantellini. A nonautonomous transcritical bifurcation problem with an application to quasi-periodic bubbles. Discrete and Continuous Dynamical Systems, 2003, 9 (1) : 209-224. doi: 10.3934/dcds.2003.9.209 |
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