Birkhoff normal forms in semi-classical inverse problems
نویسندگان
چکیده
منابع مشابه
Birkhoff Normal Forms in Semi-classical Inverse Problems
The purpose of this note is to apply the recent results on semi-classical trace formulæ [17], and on quantum Birkhoff normal forms for semi-classical Fourier Operators [12] to inverse problems. We show how the classical Birkhoff normal form can be recovered from semi-classical spectral invariants. In fact the full quantum Birkhoff normal form of the quantum Hamiltonian near a closed orbit, and ...
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• To propose a direct and “elementary” proof of the main result of [3], nameley that the semi-classical spectrum near a global minimum of the classical Hamiltonian determines the whole semi-classical Birkhoff normal form (denoted the BNF) in the non-resonant case. I believe however that the method used in [3] (trace formulas) are more general and can be applied to any non degenerate non resonan...
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• To propose a direct and “elementary” proof of the main result of [3], namely that the semi-classical spectrum near a global minimum of the classical Hamiltonian determines the whole semi-classical Birkhoff normal form (denoted the BNF) in the non-resonant case. I believe however that the method used in [3] (trace formulas) are more general and can be applied to any non degenerate non resonant...
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By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: xn+1=(2ax n)/(1+x n2)-xn-1, n=0,1,…, where x-1, x0∈(-∞,∞), and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions.
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where κ = 0, . . . , n, and λj is pure imaginary precisely when 1 ≤ j ≤ κ, and λ1, −λ1, . . . , λn, −λn are eigenvalues of Hzz(0)J with z = (x, y) and Jxj = yj = −J yj. One says that λ1, . . . , λn are non-resonant, if λ ·α ≡ λ1α1 + · · ·+λnαn 6= 0 for all multi-indices of integers α 6= 0. The Birkhoff normal form says that under the non-resonance condition on λ, there is a formal symplectic tr...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2002
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2002.v9.n3.a9