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Stochastic dynamics in a fluid--plate interaction model with the only longitudinal deformations of the plate
Smooth roughness of exponential dichotomies, revisited
1. | Institut für Mathematik, Alpen-Adria Universität Klagenfurt, Universitätsstraße 65-67, 9020 Klagenfurt, Austria |
References:
[1] |
B. Aulbach and N. Van Minh, The concept of spectral dichotomy for linear difference equations II, J. Difference Equ. Appl., 2 (1996), 251-262.
doi: 10.1080/10236199608808060. |
[2] |
B. Aulbach and T. Wanner, The Hartman-Grobman theorem for Carathéodory-type differential equations in Banach spaces, Nonlin. Analysis (TMA), 40 (2000), 91-104.
doi: 10.1016/S0362-546X(00)85006-3. |
[3] |
_______, Topological simplification of nonautonomous difference equations, J. Difference Equ. Appl., 12 (2006), 283-296.
doi: 10.1080/10236190500489384. |
[4] |
R. H. Abraham, J. E. Marsden and T. Ratiu, Manifolds, Tensor Analysis, and Applications, Second edition, Applied Mathematical Sciences, 75, Springer, Berlin etc., 1988.
doi: 10.1007/978-1-4612-1029-0. |
[5] |
L. Barreira and C. Valls, Smooth robustness of exponential dichotomies, Proc. Am. Math. Soc., 139 (2011), 999-1012.
doi: 10.1090/S0002-9939-2010-10531-2. |
[6] |
A. Carvalho, J. Langa and J. Robinson, Attractors for Infinite-Dimensional Non-autonomous Dynamical Systems, Applied Mathematical Sciences, 182, Springer, New York, 2013.
doi: 10.1007/978-1-4614-4581-4. |
[7] |
S.-N. Chow and J. K. Hale, Methods of Bifurcation Theory, Grundlehren der mathematischen Wissenschaften, 251, Springer, Berlin etc., 1996. |
[8] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lect. Notes Math., 840, Springer, Berlin etc., 1981. |
[9] |
T. Kato, Perturbation Theory for Linear Operators, Reprint of the 1980 edition, Classics in Mathematics, Springer-Verlag, Berlin, 1995. |
[10] |
P. E. Kloeden and M. Rasmussen, Nonautonomous Dynamical Systems, Mathematical Surveys and Monographs, 176, AMS, Providence, RI, 2011.
doi: 10.1090/surv/176. |
[11] |
K. J. Palmer, Transversal heteroclinic points and Cherry's example of a nonintegrable Hamiltonian system, J. Differ. Equations, 65 (1986), 321-360.
doi: 10.1016/0022-0396(86)90023-9. |
[12] |
_______, A perturbation theorem for exponential dichotomies, Proc. R. Soc. Edinb. Section A, 106 (1987), 25-37.
doi: 10.1017/S0308210500018175. |
[13] |
_______, Exponential dichotomies, the shadowing lemma and transversal homoclinic points, in Dynamics Reported. Vol. 1 (eds. U. Kirchgraber and H.-O. Walther), B.G. Teubner and John Wiley and Sons, Stuttgart/Chichester etc., 1988, 265-306. |
[14] |
C. Pötzsche, Geometric Theory of Discrete Nonautonomous Dynamical Systems, Lect. Notes Math., 2002, Springer, Berlin etc., 2010.
doi: 10.1007/978-3-642-14258-1. |
[15] |
_______, Nonautonomous bifurcation of bounded solutions I: A Lyapunov-Schmidt approach, Discrete Contin. Dyn. Syst. (Series B), 14 (2010), 739-776.
doi: 10.3934/dcdsb.2010.14.739. |
[16] |
_______, Nonautonomous continuation of bounded solutions, Commun. Pure Appl. Anal., 10 (2011), 937-961.
doi: 10.3934/cpaa.2011.10.937. |
[17] |
B. Sandstede, Verzweigungstheorie Homokliner Verdopplungen, Ph.D. thesis, Universität Stuttgart, Germany, 1993. |
[18] |
K. Sakamoto, Estimates on the strength of exponential dichotomies and application to integral manifolds, J. Differ. Equations, 107 (1994), 259-279.
doi: 10.1006/jdeq.1994.1012. |
[19] |
Y. Yi, A generalized integral manifold theorem, J. Differ. Equations, 102 (1993), 153-187.
doi: 10.1006/jdeq.1993.1026. |
[20] |
K. Yosida, Functional Analysis, Grundlehren der mathematischen Wissenschaften, 123, Springer, Berlin etc., 1980. |
show all references
References:
[1] |
B. Aulbach and N. Van Minh, The concept of spectral dichotomy for linear difference equations II, J. Difference Equ. Appl., 2 (1996), 251-262.
doi: 10.1080/10236199608808060. |
[2] |
B. Aulbach and T. Wanner, The Hartman-Grobman theorem for Carathéodory-type differential equations in Banach spaces, Nonlin. Analysis (TMA), 40 (2000), 91-104.
doi: 10.1016/S0362-546X(00)85006-3. |
[3] |
_______, Topological simplification of nonautonomous difference equations, J. Difference Equ. Appl., 12 (2006), 283-296.
doi: 10.1080/10236190500489384. |
[4] |
R. H. Abraham, J. E. Marsden and T. Ratiu, Manifolds, Tensor Analysis, and Applications, Second edition, Applied Mathematical Sciences, 75, Springer, Berlin etc., 1988.
doi: 10.1007/978-1-4612-1029-0. |
[5] |
L. Barreira and C. Valls, Smooth robustness of exponential dichotomies, Proc. Am. Math. Soc., 139 (2011), 999-1012.
doi: 10.1090/S0002-9939-2010-10531-2. |
[6] |
A. Carvalho, J. Langa and J. Robinson, Attractors for Infinite-Dimensional Non-autonomous Dynamical Systems, Applied Mathematical Sciences, 182, Springer, New York, 2013.
doi: 10.1007/978-1-4614-4581-4. |
[7] |
S.-N. Chow and J. K. Hale, Methods of Bifurcation Theory, Grundlehren der mathematischen Wissenschaften, 251, Springer, Berlin etc., 1996. |
[8] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lect. Notes Math., 840, Springer, Berlin etc., 1981. |
[9] |
T. Kato, Perturbation Theory for Linear Operators, Reprint of the 1980 edition, Classics in Mathematics, Springer-Verlag, Berlin, 1995. |
[10] |
P. E. Kloeden and M. Rasmussen, Nonautonomous Dynamical Systems, Mathematical Surveys and Monographs, 176, AMS, Providence, RI, 2011.
doi: 10.1090/surv/176. |
[11] |
K. J. Palmer, Transversal heteroclinic points and Cherry's example of a nonintegrable Hamiltonian system, J. Differ. Equations, 65 (1986), 321-360.
doi: 10.1016/0022-0396(86)90023-9. |
[12] |
_______, A perturbation theorem for exponential dichotomies, Proc. R. Soc. Edinb. Section A, 106 (1987), 25-37.
doi: 10.1017/S0308210500018175. |
[13] |
_______, Exponential dichotomies, the shadowing lemma and transversal homoclinic points, in Dynamics Reported. Vol. 1 (eds. U. Kirchgraber and H.-O. Walther), B.G. Teubner and John Wiley and Sons, Stuttgart/Chichester etc., 1988, 265-306. |
[14] |
C. Pötzsche, Geometric Theory of Discrete Nonautonomous Dynamical Systems, Lect. Notes Math., 2002, Springer, Berlin etc., 2010.
doi: 10.1007/978-3-642-14258-1. |
[15] |
_______, Nonautonomous bifurcation of bounded solutions I: A Lyapunov-Schmidt approach, Discrete Contin. Dyn. Syst. (Series B), 14 (2010), 739-776.
doi: 10.3934/dcdsb.2010.14.739. |
[16] |
_______, Nonautonomous continuation of bounded solutions, Commun. Pure Appl. Anal., 10 (2011), 937-961.
doi: 10.3934/cpaa.2011.10.937. |
[17] |
B. Sandstede, Verzweigungstheorie Homokliner Verdopplungen, Ph.D. thesis, Universität Stuttgart, Germany, 1993. |
[18] |
K. Sakamoto, Estimates on the strength of exponential dichotomies and application to integral manifolds, J. Differ. Equations, 107 (1994), 259-279.
doi: 10.1006/jdeq.1994.1012. |
[19] |
Y. Yi, A generalized integral manifold theorem, J. Differ. Equations, 102 (1993), 153-187.
doi: 10.1006/jdeq.1993.1026. |
[20] |
K. Yosida, Functional Analysis, Grundlehren der mathematischen Wissenschaften, 123, Springer, Berlin etc., 1980. |
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