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A parametrised version of Moser's modifying terms theorem
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Finite smooth normal forms and integrability of local families of vector fields
KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character
1. | Institut für Mathematik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany |
References:
[1] |
K. I. Babenko, Best approximations to a class of analytic functions, Izv. Akad. Nauk SSSR Ser. Mat., 22 (1958), 631-640. |
[2] |
E. A. Coddington and N. Levinson, "Theory of Ordinary Differential Equations,'' McGraw-Hill Book Company, Inc., New York, 1955, |
[3] |
R. A. DeVore and G. G. Lorentz, "Constructive Approximation,'' Springer-Verlag, Berlin, 1993. |
[4] |
L. Hörmander and B. Bernhardsson, An extension of Bohr's inequality,, in, 29 ().
|
[5] |
J. Moser, Combination tones for Duffing's equation, Comm. Pure Appl. Math., 18 (1965), 167-181.
doi: 10.1002/cpa.3160180116. |
[6] |
J. Moser, Convergent series expansions for quasi-periodic motions, Math. Ann., 169 (1967), 136-176.
doi: 10.1007/BF01399536. |
[7] |
H. Rüssmann, On an inequality for trigonometric polynomials in several variables, in "Analysis, et cetera (Research papers published in honor of Jürgen Moser's 60th birthday)'' (eds. P. H. Rabinowitz and E. Zehnder), Academic Press, Boston, MA (1990), 545-562. |
[8] |
H. Rüssmann, Invariant tori in non-degenerate nearly integrable Hamiltonian systems, Regul. Chaotic Dyn., 6 (2001), 119-204.
doi: 10.1070/RD2001v006n02ABEH000169. |
show all references
References:
[1] |
K. I. Babenko, Best approximations to a class of analytic functions, Izv. Akad. Nauk SSSR Ser. Mat., 22 (1958), 631-640. |
[2] |
E. A. Coddington and N. Levinson, "Theory of Ordinary Differential Equations,'' McGraw-Hill Book Company, Inc., New York, 1955, |
[3] |
R. A. DeVore and G. G. Lorentz, "Constructive Approximation,'' Springer-Verlag, Berlin, 1993. |
[4] |
L. Hörmander and B. Bernhardsson, An extension of Bohr's inequality,, in, 29 ().
|
[5] |
J. Moser, Combination tones for Duffing's equation, Comm. Pure Appl. Math., 18 (1965), 167-181.
doi: 10.1002/cpa.3160180116. |
[6] |
J. Moser, Convergent series expansions for quasi-periodic motions, Math. Ann., 169 (1967), 136-176.
doi: 10.1007/BF01399536. |
[7] |
H. Rüssmann, On an inequality for trigonometric polynomials in several variables, in "Analysis, et cetera (Research papers published in honor of Jürgen Moser's 60th birthday)'' (eds. P. H. Rabinowitz and E. Zehnder), Academic Press, Boston, MA (1990), 545-562. |
[8] |
H. Rüssmann, Invariant tori in non-degenerate nearly integrable Hamiltonian systems, Regul. Chaotic Dyn., 6 (2001), 119-204.
doi: 10.1070/RD2001v006n02ABEH000169. |
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