On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients
In this paper, we consider the effective reducibility of the quasi-periodic linear Hamiltonian system x˙=A+εQt,εx, ε∈0,ε0, where A is a constant matrix with possible multiple eigenvalues and Q(t,ε) is analytic quasi-periodic with respect to t. Under nonresonant conditions, it is proved that this sys...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/5189873 |
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| _version_ | 1850106965526577152 |
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| author | Nina Xue Wencai Zhao |
| author_facet | Nina Xue Wencai Zhao |
| author_sort | Nina Xue |
| collection | DOAJ |
| description | In this paper, we consider the effective reducibility of the quasi-periodic linear Hamiltonian system x˙=A+εQt,εx, ε∈0,ε0, where A is a constant matrix with possible multiple eigenvalues and Q(t,ε) is analytic quasi-periodic with respect to t. Under nonresonant conditions, it is proved that this system can be reduced to y˙=A⁎ε+εR⁎t,εy, ε∈0,ε⁎, where R⁎ is exponentially small in ε, and the change of variables that perform such a reduction is also quasi-periodic with the same basic frequencies as Q. |
| format | Article |
| id | doaj-art-4c789c75ec434355baa35f4635baa05f |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-4c789c75ec434355baa35f4635baa05f2025-08-20T02:38:42ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/51898735189873On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant CoefficientsNina Xue0Wencai Zhao1School of Mathematics and Information Science, Weifang University, Weifang, Shandong 261061, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, ChinaIn this paper, we consider the effective reducibility of the quasi-periodic linear Hamiltonian system x˙=A+εQt,εx, ε∈0,ε0, where A is a constant matrix with possible multiple eigenvalues and Q(t,ε) is analytic quasi-periodic with respect to t. Under nonresonant conditions, it is proved that this system can be reduced to y˙=A⁎ε+εR⁎t,εy, ε∈0,ε⁎, where R⁎ is exponentially small in ε, and the change of variables that perform such a reduction is also quasi-periodic with the same basic frequencies as Q.http://dx.doi.org/10.1155/2018/5189873 |
| spellingShingle | Nina Xue Wencai Zhao On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients Journal of Function Spaces |
| title | On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients |
| title_full | On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients |
| title_fullStr | On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients |
| title_full_unstemmed | On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients |
| title_short | On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients |
| title_sort | on the effective reducibility of a class of quasi periodic linear hamiltonian systems close to constant coefficients |
| url | http://dx.doi.org/10.1155/2018/5189873 |
| work_keys_str_mv | AT ninaxue ontheeffectivereducibilityofaclassofquasiperiodiclinearhamiltoniansystemsclosetoconstantcoefficients AT wencaizhao ontheeffectivereducibilityofaclassofquasiperiodiclinearhamiltoniansystemsclosetoconstantcoefficients |