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Gevrey normal form and effective stability of Lagrangian tori
Finite smooth normal forms and integrability of local families of vector fields
1. | Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, 33431 Boca Raton, United States |
2. | School of Mathematical Sciences, Peking University, Beijing, 100871, China |
References:
[1] |
V. I. Arnold and Yu. S. Ilyashenko, Ordinary differential equations,, Encyclopaedia of Math. Sci. 1, 1 (1988), 1.
|
[2] |
P. Bonckaert, V. Naudot and J. Yang, Linearization of germs of hyperbolic vector fields,, C. R. Math. Acad. Sci. Paris, 336 (2003), 19.
|
[3] |
I. U. Bronstein and A. Ya. Kopanskii, "Smooth Invariant Manifolds and Normal Forms,", World Scientific, (1994).
doi: 10.1142/9789812798749. |
[4] |
A. D. Bruno, "Local Methods in Nonlinear Differential Equations,", Springer-Verlag, (1989).
|
[5] |
K.-T. Chen, Equivalence and decomposition of vector fields about an elementary critical point,, Amer. J. Math., 85 (1963), 693.
doi: 10.2307/2373115. |
[6] |
Yu. S. Ilyashenko and S. Yu. Yakovenko, Finitely smooth normal forms of local families of diffeomorphisms and vector fields,, Russian Math. Surveys, 46 (1991), 1.
doi: 10.1070/RM1991v046n01ABEH002733. |
[7] |
M. Martens, V. Naudot and J. Yang, A strange attractor with large entropy in the unfodling of a low resonant degenerate homoclinic orbit,, Intern. Journ. of Bifurcation & Chaos, 16 (2006), 3509.
doi: 10.1142/S0218127406016951. |
[8] |
V. Naudot, Strange attractor in the unfolding of an inclination-flip homoclinic orbit,, Ergodic Theory and Dynamical Systems, 16 (1996), 1071.
|
[9] |
V. Naudot and J. Yang, Linearization of families of germs of hyperbolic vector fields,, Dynamical Systems, 23 (2008), 467.
doi: 10.1080/14689360802331162. |
[10] |
V. S. Samovol, Linearization of systems of differential equations in a neighbourhood of invariant toroidal manifolds,, Proc. Moscow Math. Soc., 38 (1979), 187.
|
[11] |
V. S. Samovol, A necessary and sufficient condition of smooth linearization of an autonomous planar system in a neighborhood of a critical point,, Math. Notes, 46 (1989), 543.
doi: 10.1007/BF01159105. |
[12] |
S. Sternberg, On the structure of local homeomorphisms of Euclidean $n$-space, II,, Amer. J. Math., 80 (1958), 623.
doi: 10.2307/2372774. |
[13] |
S. Sternberg, The structure of local homeomorphisms, III,, Amer. J. Math., 81 (1959), 578.
doi: 10.2307/2372915. |
[14] |
J. Yang, Polynomial normal forms for vector fields on $R^3$,, Duke Math. J., 106 (2001), 1.
doi: 10.1215/S0012-7094-01-10611-X. |
show all references
References:
[1] |
V. I. Arnold and Yu. S. Ilyashenko, Ordinary differential equations,, Encyclopaedia of Math. Sci. 1, 1 (1988), 1.
|
[2] |
P. Bonckaert, V. Naudot and J. Yang, Linearization of germs of hyperbolic vector fields,, C. R. Math. Acad. Sci. Paris, 336 (2003), 19.
|
[3] |
I. U. Bronstein and A. Ya. Kopanskii, "Smooth Invariant Manifolds and Normal Forms,", World Scientific, (1994).
doi: 10.1142/9789812798749. |
[4] |
A. D. Bruno, "Local Methods in Nonlinear Differential Equations,", Springer-Verlag, (1989).
|
[5] |
K.-T. Chen, Equivalence and decomposition of vector fields about an elementary critical point,, Amer. J. Math., 85 (1963), 693.
doi: 10.2307/2373115. |
[6] |
Yu. S. Ilyashenko and S. Yu. Yakovenko, Finitely smooth normal forms of local families of diffeomorphisms and vector fields,, Russian Math. Surveys, 46 (1991), 1.
doi: 10.1070/RM1991v046n01ABEH002733. |
[7] |
M. Martens, V. Naudot and J. Yang, A strange attractor with large entropy in the unfodling of a low resonant degenerate homoclinic orbit,, Intern. Journ. of Bifurcation & Chaos, 16 (2006), 3509.
doi: 10.1142/S0218127406016951. |
[8] |
V. Naudot, Strange attractor in the unfolding of an inclination-flip homoclinic orbit,, Ergodic Theory and Dynamical Systems, 16 (1996), 1071.
|
[9] |
V. Naudot and J. Yang, Linearization of families of germs of hyperbolic vector fields,, Dynamical Systems, 23 (2008), 467.
doi: 10.1080/14689360802331162. |
[10] |
V. S. Samovol, Linearization of systems of differential equations in a neighbourhood of invariant toroidal manifolds,, Proc. Moscow Math. Soc., 38 (1979), 187.
|
[11] |
V. S. Samovol, A necessary and sufficient condition of smooth linearization of an autonomous planar system in a neighborhood of a critical point,, Math. Notes, 46 (1989), 543.
doi: 10.1007/BF01159105. |
[12] |
S. Sternberg, On the structure of local homeomorphisms of Euclidean $n$-space, II,, Amer. J. Math., 80 (1958), 623.
doi: 10.2307/2372774. |
[13] |
S. Sternberg, The structure of local homeomorphisms, III,, Amer. J. Math., 81 (1959), 578.
doi: 10.2307/2372915. |
[14] |
J. Yang, Polynomial normal forms for vector fields on $R^3$,, Duke Math. J., 106 (2001), 1.
doi: 10.1215/S0012-7094-01-10611-X. |
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