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A NOTE ON QUASI-PERIODIC PERTURBATIONS OF ELLIPTIC EQUILIBRIUM POINTS

Houyu Zhao
대한수학회 (The Korean Mathematical Society)|2012.12|대한수학회보 (Bulletin of the KMS)|제49권 제6호|pp. 1223-1240

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참고문헌

키워드

quasi-periodic perturbationselliptic pointsquasi-periodic solutionsnonresonant conditionsmall divisorsquasi-periodic Floquet theoremKAM theory
주제분류수학

초록

The system $$\dot{x}=(A+\varepsilon Q(t,\varepsilon))x+\varepsilon g(t,\varepsilon)+ h(x,t,\varepsilon),$$ where $A$ is elliptic whose eigenvalues are not necessarily simple and $h$ is ${\mathcal{O}}(x^2)$. It is proved that, under suitable hypothesis of analyticity, for most values of the frequencies, the system is reducible.

Abstract

The system $$\dot{x}=(A+\varepsilon Q(t,\varepsilon))x+\varepsilon g(t,\varepsilon)+ h(x,t,\varepsilon),$$ where $A$ is elliptic whose eigenvalues are not necessarily simple and $h$ is ${\mathcal{O}}(x^2)$. It is proved that, under suitable hypothesis of analyticity, for most values of the frequencies, the system is reducible.

참고문헌 (16)

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  11. J. Moser, "Convergent series expansions for quasi-periodic motions", Math. Ann, 169, pp.136~176 (1967)
  12. J. Moser, "On the stationary Schr¨odinger equation with a quasiperiodic potential", Phys. A, 124(1), pp.535~542 (1984)
  13. H. R¨ussmann, "On the one dimensional Schr¨odinger equation with a quasiperiodic potential, Nonlinear dynamics (Internat. Conf., New York, 1979)", Ann. New York Acad. Sci., 357, pp.90~107 (1980)
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