Huang, Peng Existence of invariant curves for degenerate almost periodic reversible mappings. (English) Zbl 1508.37073 Discrete Contin. Dyn. Syst. 42, No. 10, 4853-4886 (2022). Reviewer: Pengfei Zhang (Norman) MSC: 37J40 37J35 37E40 PDFBibTeX XMLCite \textit{P. Huang}, Discrete Contin. Dyn. Syst. 42, No. 10, 4853--4886 (2022; Zbl 1508.37073) Full Text: DOI
Huang, Peng Existence of invariant curves for degenerate quasi-periodic reversible mappings. (English) Zbl 1504.37076 Taiwanese J. Math. 26, No. 4, 765-798 (2022). MSC: 37J40 37E40 70K43 PDFBibTeX XMLCite \textit{P. Huang}, Taiwanese J. Math. 26, No. 4, 765--798 (2022; Zbl 1504.37076) Full Text: DOI Link
Marnat, Antoine Diophantine sets and Dirichlet improvability. (English) Zbl 1508.11069 Mosc. J. Comb. Number Theory 11, No. 2, 189-196 (2022). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11J13 11H06 PDFBibTeX XMLCite \textit{A. Marnat}, Mosc. J. Comb. Number Theory 11, No. 2, 189--196 (2022; Zbl 1508.11069) Full Text: DOI arXiv
Bounemoura, Abed; Chavaudret, Claire; Liang, Shuqing Reducibility of ultra-differentiable quasiperiodic cocycles under an adapted arithmetic condition. (English) Zbl 07352298 Proc. Am. Math. Soc. 149, No. 7, 2999-3012 (2021). MSC: 37J40 37A44 37C40 37C55 PDFBibTeX XMLCite \textit{A. Bounemoura} et al., Proc. Am. Math. Soc. 149, No. 7, 2999--3012 (2021; Zbl 07352298) Full Text: DOI arXiv
Si, Wen; Si, Jianguo Linearization of a quasi-periodically forced flow on \(\mathbb T^m\) under Brjuno-Rüssmann non-resonant condition. (English) Zbl 1397.37066 Appl. Anal. 97, No. 12, 2001-2024 (2018). MSC: 37J40 70H08 70K43 PDFBibTeX XMLCite \textit{W. Si} and \textit{J. Si}, Appl. Anal. 97, No. 12, 2001--2024 (2018; Zbl 1397.37066) Full Text: DOI
Si, Wen; Si, Jianguo Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems. (English) Zbl 1401.37067 Nonlinearity 31, No. 6, 2361-2418 (2018). Reviewer: Manuel de León (Madrid) MSC: 37J40 34C27 34E20 70H12 70H08 PDFBibTeX XMLCite \textit{W. Si} and \textit{J. Si}, Nonlinearity 31, No. 6, 2361--2418 (2018; Zbl 1401.37067) Full Text: DOI
Zhang, Dongfeng; Xu, Junxiang; Wang, Xiaocai A new KAM iteration with nearly infinitely small steps in reversible systems of polynomial character. (English) Zbl 1392.37048 Qual. Theory Dyn. Syst. 17, No. 1, 271-289 (2018). MSC: 37J40 47A55 70K43 PDFBibTeX XMLCite \textit{D. Zhang} et al., Qual. Theory Dyn. Syst. 17, No. 1, 271--289 (2018; Zbl 1392.37048) Full Text: DOI
Si, Wen; Si, Jianguo Elliptic-type degenerate invariant tori for quasi-periodically forced four-dimensional non-conservative systems. (English) Zbl 1381.37074 J. Math. Anal. Appl. 460, No. 1, 164-202 (2018). MSC: 37J40 37J05 PDFBibTeX XMLCite \textit{W. Si} and \textit{J. Si}, J. Math. Anal. Appl. 460, No. 1, 164--202 (2018; Zbl 1381.37074) Full Text: DOI
Zhang, Dongfeng; Liang, Jianli On high dimensional Schrödinger equation with quasi-periodic potentials. (English) Zbl 1370.70038 J. Dyn. Control Syst. 23, No. 3, 655-666 (2017). MSC: 70H08 37J40 34C27 PDFBibTeX XMLCite \textit{D. Zhang} and \textit{J. Liang}, J. Dyn. Control Syst. 23, No. 3, 655--666 (2017; Zbl 1370.70038) Full Text: DOI
Si, Wen; Si, Jianguo Construction of response solutions for two classes of quasi-periodically forced four-dimensional nonlinear systems with degenerate equilibrium point under small perturbations. (English) Zbl 1364.37130 J. Differ. Equations 262, No. 9, 4771-4822 (2017). Reviewer: Petro Feketa (Erfurt) MSC: 37J40 34C27 34E20 PDFBibTeX XMLCite \textit{W. Si} and \textit{J. Si}, J. Differ. Equations 262, No. 9, 4771--4822 (2017; Zbl 1364.37130) Full Text: DOI
Zhang, Dongfeng; Xu, Junxiang; Wu, Hao On invariant tori with prescribed frequency in Hamiltonian systems. (English) Zbl 1364.70034 Adv. Nonlinear Stud. 16, No. 4, 719-735 (2016). Reviewer: Xiang Zhang (Shanghai) MSC: 70H08 37J40 34C27 PDFBibTeX XMLCite \textit{D. Zhang} et al., Adv. Nonlinear Stud. 16, No. 4, 719--735 (2016; Zbl 1364.70034) Full Text: DOI
Bounemoura, Abed Non-degenerate Liouville tori are KAM stable. (English) Zbl 1336.37048 Adv. Math. 292, 42-51 (2016). Reviewer: William J. Satzer jun. (St. Paul) MSC: 37J40 37J25 PDFBibTeX XMLCite \textit{A. Bounemoura}, Adv. Math. 292, 42--51 (2016; Zbl 1336.37048) Full Text: DOI arXiv
Zhang, Dongfeng; Xu, Junxiang On invariant tori of vector field under weaker non-degeneracy condition. (English) Zbl 1358.37101 NoDEA, Nonlinear Differ. Equ. Appl. 22, No. 5, 1381-1394 (2015). MSC: 37J40 70H08 70K43 PDFBibTeX XMLCite \textit{D. Zhang} and \textit{J. Xu}, NoDEA, Nonlinear Differ. Equ. Appl. 22, No. 5, 1381--1394 (2015; Zbl 1358.37101) Full Text: DOI
Bounemoura, Abed; Fischler, Stéphane The classical KAM theorem for Hamiltonian systems via rational approximations. (English) Zbl 1339.37042 Regul. Chaotic Dyn. 19, No. 2, 251-265 (2014). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 37J25 37J40 70H08 70H09 PDFBibTeX XMLCite \textit{A. Bounemoura} and \textit{S. Fischler}, Regul. Chaotic Dyn. 19, No. 2, 251--265 (2014; Zbl 1339.37042) Full Text: DOI arXiv
Zhang, Dongfeng; Xu, Junxiang Invariant curves of analytic reversible mappings under Brjuno-Rüssmann’s non-resonant condition. (English) Zbl 1320.47009 J. Dyn. Differ. Equations 26, No. 4, 989-1005 (2014). Reviewer: Adriana Buică (Cluj-Napoca) MSC: 47A56 47A60 47A68 PDFBibTeX XMLCite \textit{D. Zhang} and \textit{J. Xu}, J. Dyn. Differ. Equations 26, No. 4, 989--1005 (2014; Zbl 1320.47009) Full Text: DOI
Bounemoura, Abed; Fischler, Stéphane A Diophantine duality applied to the KAM and Nekhoroshev theorems. (English) Zbl 1308.37028 Math. Z. 275, No. 3-4, 1135-1167 (2013). Reviewer: Angel Zhivkov (Sofia) MSC: 37J40 34C20 70H08 PDFBibTeX XMLCite \textit{A. Bounemoura} and \textit{S. Fischler}, Math. Z. 275, No. 3--4, 1135--1167 (2013; Zbl 1308.37028) Full Text: DOI arXiv
Féjoz, Jacques A proof of the invariant torus theorem of Kolmogorov. (English) Zbl 1252.70033 Regul. Chaotic Dyn. 17, No. 1, 1-5 (2012). MSC: 70F15 PDFBibTeX XMLCite \textit{J. Féjoz}, Regul. Chaotic Dyn. 17, No. 1, 1--5 (2012; Zbl 1252.70033) Full Text: DOI arXiv
Hanßmann, Heinz Non-degeneracy conditions in KAM theory. (English) Zbl 1253.37058 Indag. Math., New Ser. 22, No. 3-4, 241-256 (2011). MSC: 37J40 PDFBibTeX XMLCite \textit{H. Hanßmann}, Indag. Math., New Ser. 22, No. 3--4, 241--256 (2011; Zbl 1253.37058) Full Text: DOI
Pöschel, Jürgen KAM à la R. (English) Zbl 1219.37044 Regul. Chaotic Dyn. 16, No. 1-2, 17-23 (2011). MSC: 37J40 70H08 70K43 PDFBibTeX XMLCite \textit{J. Pöschel}, Regul. Chaotic Dyn. 16, No. 1--2, 17--23 (2011; Zbl 1219.37044) Full Text: DOI arXiv