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Exponentially small splitting for whiskered tori in Hamiltonian systems: flow-box coordinates and upper bounds
The flow of classical mechanical cubic potential systems
| 1. | Department of Mathematics, Facultad de Ciencias, UNAM, Ciudad Universitaria, México, D.F. 04510, Mexico |
| 2. | Department of Mathematics, UAM-I, P.O.Box 55-534, México, D.F. 09340, MEX, Mexico |
| 3. | Department of Mathematics, Universidade Federal de Pernambuco, Cidade Universitaria, Recife-Pe, Brazil |
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Jaume Llibre, Yuzhou Tian. Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4. Discrete and Continuous Dynamical Systems - B, 2022, 27 (8) : 4305-4316. doi: 10.3934/dcdsb.2021228 |
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Guillaume Duval, Andrzej J. Maciejewski. Integrability of Hamiltonian systems with homogeneous potentials of degrees $\pm 2$. An application of higher order variational equations. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4589-4615. doi: 10.3934/dcds.2014.34.4589 |
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Yilei Tang, Long Wang, Xiang Zhang. Center of planar quintic quasi--homogeneous polynomial differential systems. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 2177-2191. doi: 10.3934/dcds.2015.35.2177 |
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Francisco Braun, Jaume Llibre, Ana Cristina Mereu. Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems. Discrete and Continuous Dynamical Systems, 2016, 36 (10) : 5245-5255. doi: 10.3934/dcds.2016029 |
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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 |
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Amadeu Delshams, Pere Gutiérrez, Tere M. Seara. Exponentially small splitting for whiskered tori in Hamiltonian systems: flow-box coordinates and upper bounds. Discrete and Continuous Dynamical Systems, 2004, 11 (4) : 785-826. doi: 10.3934/dcds.2004.11.785 |
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Yilei Tang. Global dynamics and bifurcation of planar piecewise smooth quadratic quasi-homogeneous differential systems. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 2029-2046. doi: 10.3934/dcds.2018082 |
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