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Intermediate $\beta$-shifts of finite type
Polynomial and linearized normal forms for almost periodic differential systems
1. | School of Mathematics, Peking University, Beijing 100871 |
2. | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia |
3. | Department of Mathematics, Southeast University, Nanjing 210096, Jiangsu, China |
References:
[1] |
L. Arnold, Random Dynamical Systems,, Springer Monographs in Mathematics, (1998).
doi: 10.1007/978-3-662-12878-7. |
[2] |
D. Bainov and P. Simenov, Integral Inequalities and Applications,, Kluwer academic publishers, (1992).
doi: 10.1007/978-94-015-8034-2. |
[3] |
Yn. N. Bibikov, Local Theory of Nonlinear Analytic Ordinary Differential Equations,, Lecture Notes in Math., 702 (1979).
|
[4] |
K. T. Chen, Equivalence and decomposition of vector fields about an elementary critical point,, Am. J. Math., 85 (1963), 693.
doi: 10.2307/2373115. |
[5] |
W. A. Coppel, Dichotomies in Stability Theory,, Lecture Notes in Mathematics, (1978).
|
[6] |
H. Dulac, Solution d'un systeme d'equations differentielles dans le voisinage de valeurs singulieres,, Bull. Soc. Math. Fr., 40 (1912), 324.
|
[7] |
A. M. Fink, Almost Periodic Differential Equations,, Lecture Notes in Math., 377 (1974).
|
[8] |
J. K. Hale, Ordinary Differential Equations, Second edition,, Robert E. Krieger Publishing Co., (1980).
|
[9] |
Yu. S. Il'yashenko and S. Yu. Yakovenko, Finitely-smooth normal forms of local families of diffeomorphisms and vector fields,, Russian Math Sur., 46 (1991), 1.
doi: 10.1070/RM1991v046n01ABEH002733. |
[10] |
W. Li and K. Lu, Poincaré theorems for random dynamical systems,, Ergodic Theory Dynam. Systems, 25 (2005), 1221.
doi: 10.1017/S014338570400094X. |
[11] |
W. Li and K. Lu, Sternberg theorems for random dynamical systems,, Comm. Pure Appl. Math., 58 (2005), 941.
doi: 10.1002/cpa.20083. |
[12] |
H. Poincaré, Thesis, 1879, also Oeuvres I,, Gauthier Villars, (1928), 59. Google Scholar |
[13] |
R. J. Sacker and G. R. Sell, A spectral theory for linear differential systems,, J. Diff. Equ., 27 (1978), 320.
doi: 10.1016/0022-0396(78)90057-8. |
[14] |
S. Siegmund, Normal forms for nonautonomous difference equations. Advances in difference equations, IV,, Comput. Math. Appl., 45 (2003), 1059.
doi: 10.1016/S0898-1221(03)00085-3. |
[15] |
S. Stenberg, Finite Lie groups and the formal aspects of dynamical systems,, J. Math. Mech., 10 (1961), 451.
|
[16] |
F. Takens, Normal forms for certain singularities of vector fields,, An. Inst. Fourier., 23 (1973), 163.
doi: 10.5802/aif.467. |
[17] |
A. Vanderbauwhede, Center manifolds and their basic properties. An introduction,, Delft Progr. Rep., 12 (1988), 57.
|
show all references
References:
[1] |
L. Arnold, Random Dynamical Systems,, Springer Monographs in Mathematics, (1998).
doi: 10.1007/978-3-662-12878-7. |
[2] |
D. Bainov and P. Simenov, Integral Inequalities and Applications,, Kluwer academic publishers, (1992).
doi: 10.1007/978-94-015-8034-2. |
[3] |
Yn. N. Bibikov, Local Theory of Nonlinear Analytic Ordinary Differential Equations,, Lecture Notes in Math., 702 (1979).
|
[4] |
K. T. Chen, Equivalence and decomposition of vector fields about an elementary critical point,, Am. J. Math., 85 (1963), 693.
doi: 10.2307/2373115. |
[5] |
W. A. Coppel, Dichotomies in Stability Theory,, Lecture Notes in Mathematics, (1978).
|
[6] |
H. Dulac, Solution d'un systeme d'equations differentielles dans le voisinage de valeurs singulieres,, Bull. Soc. Math. Fr., 40 (1912), 324.
|
[7] |
A. M. Fink, Almost Periodic Differential Equations,, Lecture Notes in Math., 377 (1974).
|
[8] |
J. K. Hale, Ordinary Differential Equations, Second edition,, Robert E. Krieger Publishing Co., (1980).
|
[9] |
Yu. S. Il'yashenko and S. Yu. Yakovenko, Finitely-smooth normal forms of local families of diffeomorphisms and vector fields,, Russian Math Sur., 46 (1991), 1.
doi: 10.1070/RM1991v046n01ABEH002733. |
[10] |
W. Li and K. Lu, Poincaré theorems for random dynamical systems,, Ergodic Theory Dynam. Systems, 25 (2005), 1221.
doi: 10.1017/S014338570400094X. |
[11] |
W. Li and K. Lu, Sternberg theorems for random dynamical systems,, Comm. Pure Appl. Math., 58 (2005), 941.
doi: 10.1002/cpa.20083. |
[12] |
H. Poincaré, Thesis, 1879, also Oeuvres I,, Gauthier Villars, (1928), 59. Google Scholar |
[13] |
R. J. Sacker and G. R. Sell, A spectral theory for linear differential systems,, J. Diff. Equ., 27 (1978), 320.
doi: 10.1016/0022-0396(78)90057-8. |
[14] |
S. Siegmund, Normal forms for nonautonomous difference equations. Advances in difference equations, IV,, Comput. Math. Appl., 45 (2003), 1059.
doi: 10.1016/S0898-1221(03)00085-3. |
[15] |
S. Stenberg, Finite Lie groups and the formal aspects of dynamical systems,, J. Math. Mech., 10 (1961), 451.
|
[16] |
F. Takens, Normal forms for certain singularities of vector fields,, An. Inst. Fourier., 23 (1973), 163.
doi: 10.5802/aif.467. |
[17] |
A. Vanderbauwhede, Center manifolds and their basic properties. An introduction,, Delft Progr. Rep., 12 (1988), 57.
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