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Unsteady flows of non-Newtonian fluids in generalized Orlicz spaces
On quasi-periodic perturbations of hyperbolic-type degenerate equilibrium point of a class of planar systems
| 1. | Department of Mathematics, Southeast University, Nanjing 210096 |
References:
| [1] |
H. W. Broer, G. B. Huitema, F. Takens and B. L. J. Braaksma, Unfoldings and bifurcations of quasi-periodic tori, Mem. Amer. Math. Soc., 83 (1990), viii+175. |
| [2] |
H. W. Broer, G. B. Huitema and M. B. Sevryuk, "Quasi-periodic Motions in Families of Dynamical Systems," Lecture Notes in Mathematics, 1645, 1996. |
| [3] |
C. Q. Cheng, Lower diemsional invariant tori in the regions of instability of nearly integrable hamiltonian systems, Commun. Math. Phys., 203 (1999), 385-419.
doi: 10.1007/s002200050618. |
| [4] |
L. H. Eliasson, Almost reducibility of linear quasi-periodic systems, Smooth ergodic theory and its applications (Seattle, WA, 1999), 679-705, Proc. Sympos. Pure Math., 69, Amer. Math. Soc., Providence, RI, (2001). |
| [5] |
S. M. Graff, On the conservation of hyperbolic invariant tori for hamiltonian systems, J. Differential Equations, 15 (1974), 1-69. |
| [6] |
H. Her and J. You, Full measure reducibility for generic one-parameter family of quasi-periodic linear systems, J. Dynam. Differential Equations, 20 (2008), 831-866.
doi: 10.1007/s10884-008-9113-6. |
| [7] |
A. Jorba and C. Simó, On the reducibility of linear differential equations with quasiperiodic coefficients, J. Differential Equations, 98 (1992), 111-124.
doi: 10.1016/0022-0396(92)90107-X. |
| [8] |
A. Jorba and C. Simó, On quasi-periodic perturbations of elliptic equilibrium points, SIAM J. Math. Anal., 27 (1996), 1704-1737.
doi: 10.1137/S0036141094276913. |
| [9] |
J. Moser, Convergent series expansions for quasi-periodic motions, Math. Ann., 169 (1976), 136-176. |
| [10] |
J. Pöschel, On elliptic lower dimensional tori in hamiltonian systems, Math. Z., 202 (1989), 559-608.
doi: 10.1007/BF01221590. |
| [11] |
W. Rudin, "Real and Complex Analysis," Third Edition, McGraw-Hill Compnies, Inc., 2003. |
| [12] |
Junxiang Xu and Qin Zheng, On the reducibility of linear differential equations with quasi-periodic coefficients which are degenerate, Proc. Amer. Math. Soc., 126 (1998), 1445-1451.
doi: 10.1090/S0002-9939-98-04523-7. |
| [13] |
Junxiang Xu, Persistence of Floquet invariant tori for a class of non-conservative dynamical systems, Proc. Amer. Math. Soc., 135 (2007), 805-814.
doi: 10.1090/S0002-9939-06-08529-7. |
| [14] |
Junxiang Xu and Shunjun Jiang, Reducibility for a class of nonlinear quasi-periodic differential equations with degenerate equilibrium point under small perturbation, Ergodic Theory and Dynamical Systems, 31 (2011), 599-611.
doi: 10.1017/S0143385709001114. |
| [15] |
Junxiang Xu, On small perturbation of two-dimensional quasi-periodic systems with hyperbolic-type degenerate equilibrium point, J. Differential Equations, 250 (2011), 551-571.
doi: 10.1016/j.jde.2010.09.030. |
| [16] |
J. You, A KAM theorem for hyperbolic-type degenerate lower dimensional tori in Hamiltonian systems, Commun. Math. Phys., 192 (1998), 145-168.
doi: 10.1007/s002200050294. |
show all references
References:
| [1] |
H. W. Broer, G. B. Huitema, F. Takens and B. L. J. Braaksma, Unfoldings and bifurcations of quasi-periodic tori, Mem. Amer. Math. Soc., 83 (1990), viii+175. |
| [2] |
H. W. Broer, G. B. Huitema and M. B. Sevryuk, "Quasi-periodic Motions in Families of Dynamical Systems," Lecture Notes in Mathematics, 1645, 1996. |
| [3] |
C. Q. Cheng, Lower diemsional invariant tori in the regions of instability of nearly integrable hamiltonian systems, Commun. Math. Phys., 203 (1999), 385-419.
doi: 10.1007/s002200050618. |
| [4] |
L. H. Eliasson, Almost reducibility of linear quasi-periodic systems, Smooth ergodic theory and its applications (Seattle, WA, 1999), 679-705, Proc. Sympos. Pure Math., 69, Amer. Math. Soc., Providence, RI, (2001). |
| [5] |
S. M. Graff, On the conservation of hyperbolic invariant tori for hamiltonian systems, J. Differential Equations, 15 (1974), 1-69. |
| [6] |
H. Her and J. You, Full measure reducibility for generic one-parameter family of quasi-periodic linear systems, J. Dynam. Differential Equations, 20 (2008), 831-866.
doi: 10.1007/s10884-008-9113-6. |
| [7] |
A. Jorba and C. Simó, On the reducibility of linear differential equations with quasiperiodic coefficients, J. Differential Equations, 98 (1992), 111-124.
doi: 10.1016/0022-0396(92)90107-X. |
| [8] |
A. Jorba and C. Simó, On quasi-periodic perturbations of elliptic equilibrium points, SIAM J. Math. Anal., 27 (1996), 1704-1737.
doi: 10.1137/S0036141094276913. |
| [9] |
J. Moser, Convergent series expansions for quasi-periodic motions, Math. Ann., 169 (1976), 136-176. |
| [10] |
J. Pöschel, On elliptic lower dimensional tori in hamiltonian systems, Math. Z., 202 (1989), 559-608.
doi: 10.1007/BF01221590. |
| [11] |
W. Rudin, "Real and Complex Analysis," Third Edition, McGraw-Hill Compnies, Inc., 2003. |
| [12] |
Junxiang Xu and Qin Zheng, On the reducibility of linear differential equations with quasi-periodic coefficients which are degenerate, Proc. Amer. Math. Soc., 126 (1998), 1445-1451.
doi: 10.1090/S0002-9939-98-04523-7. |
| [13] |
Junxiang Xu, Persistence of Floquet invariant tori for a class of non-conservative dynamical systems, Proc. Amer. Math. Soc., 135 (2007), 805-814.
doi: 10.1090/S0002-9939-06-08529-7. |
| [14] |
Junxiang Xu and Shunjun Jiang, Reducibility for a class of nonlinear quasi-periodic differential equations with degenerate equilibrium point under small perturbation, Ergodic Theory and Dynamical Systems, 31 (2011), 599-611.
doi: 10.1017/S0143385709001114. |
| [15] |
Junxiang Xu, On small perturbation of two-dimensional quasi-periodic systems with hyperbolic-type degenerate equilibrium point, J. Differential Equations, 250 (2011), 551-571.
doi: 10.1016/j.jde.2010.09.030. |
| [16] |
J. You, A KAM theorem for hyperbolic-type degenerate lower dimensional tori in Hamiltonian systems, Commun. Math. Phys., 192 (1998), 145-168.
doi: 10.1007/s002200050294. |
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