Danesi, Veronica; Sansottera, Marco; Paleari, Simone; Penati, Tiziano Continuation of spatially localized periodic solutions in discrete NLS lattices via normal forms. (English) Zbl 07474647 Commun. Nonlinear Sci. Numer. Simul. 108, Article ID 106266, 23 p. (2022). MSC: 37Kxx 37Jxx 35Qxx PDF BibTeX XML Cite \textit{V. Danesi} et al., Commun. Nonlinear Sci. Numer. Simul. 108, Article ID 106266, 23 p. (2022; Zbl 07474647) Full Text: DOI arXiv OpenURL
Si, Wen; Yi, Yingfei Completely degenerate responsive tori in Hamiltonian systems. (English) Zbl 1455.37048 Nonlinearity 33, No. 11, 6072-6098 (2020). MSC: 37J40 70H08 70K43 PDF BibTeX XML Cite \textit{W. Si} and \textit{Y. Yi}, Nonlinearity 33, No. 11, 6072--6098 (2020; Zbl 1455.37048) Full Text: DOI OpenURL
Sansottera, Marco; Danesi, V.; Penati, T.; Paleari, S. On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori. (English) Zbl 1453.37059 Commun. Nonlinear Sci. Numer. Simul. 90, Article ID 105360, 22 p. (2020). MSC: 37J40 37K55 70H08 70K43 PDF BibTeX XML Cite \textit{M. Sansottera} et al., Commun. Nonlinear Sci. Numer. Simul. 90, Article ID 105360, 22 p. (2020; Zbl 1453.37059) Full Text: DOI arXiv OpenURL
Yang, Lianpeng; Li, Xiong Existence of periodically invariant tori on resonant surfaces for twist mappings. (English) Zbl 1432.37071 Discrete Contin. Dyn. Syst. 40, No. 3, 1389-1409 (2020). MSC: 37E40 37J40 PDF BibTeX XML Cite \textit{L. Yang} and \textit{X. Li}, Discrete Contin. Dyn. Syst. 40, No. 3, 1389--1409 (2020; Zbl 1432.37071) Full Text: DOI OpenURL
Zhang, Dongfeng; Xu, Xindong On the linearization of vector fields on a torus with prescribed frequency. (English) Zbl 1455.37049 Topol. Methods Nonlinear Anal. 54, No. 2A, 649-663 (2019). Reviewer: Valerii V. Obukhovskij (Voronezh) MSC: 37J40 34C27 70H08 70K43 PDF BibTeX XML Cite \textit{D. Zhang} and \textit{X. Xu}, Topol. Methods Nonlinear Anal. 54, No. 2A, 649--663 (2019; Zbl 1455.37049) Full Text: DOI Euclid OpenURL
Palacián, J. F.; Vidal, C.; Vidarte, J.; Yanguas, P. Periodic solutions, KAM tori and bifurcations in a cosmology-inspired potential. (English) Zbl 1435.37088 Nonlinearity 32, No. 9, 3406-3444 (2019). Reviewer: Giuseppe Gaeta (Milano) MSC: 37J40 37J46 37J20 34C15 70K65 34C23 70K28 70K30 70K43 PDF BibTeX XML Cite \textit{J. F. Palacián} et al., Nonlinearity 32, No. 9, 3406--3444 (2019; Zbl 1435.37088) Full Text: DOI Link OpenURL
Penati, Tiziano; Sansottera, M.; Danesi, V. On the continuation of degenerate periodic orbits via normal form: full dimensional resonant tori. (English) Zbl 1473.70034 Commun. Nonlinear Sci. Numer. Simul. 61, 198-224 (2018). MSC: 70H12 70H09 34C25 37N05 PDF BibTeX XML Cite \textit{T. Penati} et al., Commun. Nonlinear Sci. Numer. Simul. 61, 198--224 (2018; Zbl 1473.70034) Full Text: DOI arXiv Link OpenURL
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 PDF BibTeX XML Cite \textit{W. Si} and \textit{J. Si}, Appl. Anal. 97, No. 12, 2001--2024 (2018; Zbl 1397.37066) Full Text: DOI OpenURL
Geng, Jiansheng; Zhou, Shidi An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation. (English) Zbl 1408.37127 J. Math. Phys. 59, No. 7, 072702, 25 p. (2018). MSC: 37K55 74K10 35B34 70K43 PDF BibTeX XML Cite \textit{J. Geng} and \textit{S. Zhou}, J. Math. Phys. 59, No. 7, 072702, 25 p. (2018; Zbl 1408.37127) Full Text: DOI arXiv OpenURL
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 PDF BibTeX XML Cite \textit{D. Zhang} et al., Qual. Theory Dyn. Syst. 17, No. 1, 271--289 (2018; Zbl 1392.37048) Full Text: DOI OpenURL
Xu, Lu; Li, Yong; Yi, Yingfei Poincaré-Treshchev mechanism in multi-scale, nearly integrable Hamiltonian systems. (English) Zbl 1407.37100 J. Nonlinear Sci. 28, No. 1, 337-369 (2018). MSC: 37J40 70H08 37N05 PDF BibTeX XML Cite \textit{L. Xu} et al., J. Nonlinear Sci. 28, No. 1, 337--369 (2018; Zbl 1407.37100) Full Text: DOI OpenURL
Sevryuk, Mikhail B. Families of invariant tori in KAM theory: interplay of integer characteristics. (English) Zbl 1384.37078 Regul. Chaotic Dyn. 22, No. 6, 603-615 (2017). Reviewer: Giuseppe Gaeta (Milano) MSC: 37J40 70H08 70H33 70K43 PDF BibTeX XML Cite \textit{M. B. Sevryuk}, Regul. Chaotic Dyn. 22, No. 6, 603--615 (2017; Zbl 1384.37078) Full Text: DOI arXiv OpenURL
Ji, J. C.; Brown, Terry Periodic and chaotic motion of a time-delayed nonlinear system under two coexisting families of additive resonances. (English) Zbl 1367.70045 Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 5, Article ID 1750066, 15 p. (2017). MSC: 70K20 70K55 70K30 34K60 70K40 70K42 70K50 70K43 PDF BibTeX XML Cite \textit{J. C. Ji} and \textit{T. Brown}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 5, Article ID 1750066, 15 p. (2017; Zbl 1367.70045) Full Text: DOI OpenURL
de la Llave, Rafael; Su, Xifeng; Zhang, Lei Resonant equilibrium configurations in quasi-periodic media: KAM theory. (English) Zbl 1404.70057 SIAM J. Math. Anal. 49, No. 1, 597-625 (2017). MSC: 70K43 37J40 52C23 70H08 PDF BibTeX XML Cite \textit{R. de la Llave} et al., SIAM J. Math. Anal. 49, No. 1, 597--625 (2017; Zbl 1404.70057) Full Text: DOI arXiv OpenURL
Xu, Lu; Li, Yong; Yi, Yingfei Lower-dimensional tori in multi-scale, nearly integrable Hamiltonian systems. (English) Zbl 1380.37118 Ann. Henri Poincaré 18, No. 1, 53-83 (2017). Reviewer: Yulianna Perepelkina (Moskva) MSC: 37J40 70H08 37N05 70F15 PDF BibTeX XML Cite \textit{L. Xu} et al., Ann. Henri Poincaré 18, No. 1, 53--83 (2017; Zbl 1380.37118) Full Text: DOI OpenURL
Palacián, J. F.; Vidal, C.; Vidarte, J.; Yanguas, P. Periodic solutions and KAM tori in a triaxial potential. (English) Zbl 1358.37100 SIAM J. Appl. Dyn. Syst. 16, No. 1, 159-187 (2017). MSC: 37J40 34C15 34C20 34C25 70K65 70H08 37N05 PDF BibTeX XML Cite \textit{J. F. Palacián} et al., SIAM J. Appl. Dyn. Syst. 16, No. 1, 159--187 (2017; Zbl 1358.37100) Full Text: DOI OpenURL
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 PDF BibTeX XML Cite \textit{D. Zhang} et al., Adv. Nonlinear Stud. 16, No. 4, 719--735 (2016; Zbl 1364.70034) Full Text: DOI OpenURL
de la Llave, Rafael; Su, Xifeng; Zhang, Lei Resonant equilibrium configurations in quasi-periodic media: perturbative expansions. (English) Zbl 1382.70022 J. Stat. Phys. 162, No. 6, 1522-1538 (2016). MSC: 70K43 37J50 37J40 70H08 PDF BibTeX XML Cite \textit{R. de la Llave} et al., J. Stat. Phys. 162, No. 6, 1522--1538 (2016; Zbl 1382.70022) Full Text: DOI arXiv OpenURL
Medvedev, A. G.; Neishtadt, A. I.; Treschev, D. V. Lagrangian tori near resonances of near-integrable Hamiltonian systems. (English) Zbl 1378.70021 Nonlinearity 28, No. 7, 2105-2130 (2015). MSC: 70H08 37J40 PDF BibTeX XML Cite \textit{A. G. Medvedev} et al., Nonlinearity 28, No. 7, 2105--2130 (2015; Zbl 1378.70021) Full Text: DOI arXiv Link OpenURL
Procesi, C.; Procesi, M. A KAM algorithm for the resonant non-linear Schrödinger equation. (English) Zbl 1312.37047 Adv. Math. 272, 399-470 (2015). Reviewer: Dmitry Pelinovsky (Hamilton) MSC: 37K55 35Q55 PDF BibTeX XML Cite \textit{C. Procesi} and \textit{M. Procesi}, Adv. Math. 272, 399--470 (2015; Zbl 1312.37047) Full Text: DOI arXiv OpenURL
Yuan, Xiaoping Recent progress on nonlinear wave equations via KAM theory. (English) Zbl 1196.37115 Tang, Shanjian (ed.) et al., Control theory and related topics. In memory of Professor Xunjing Li, Fudan, China, June 3–5, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-270-582-2/hbk). 387-395 (2007). Reviewer: Hu Chuangan (Cupertino) MSC: 37K55 35L70 PDF BibTeX XML Cite \textit{X. Yuan}, in: Control theory and related topics. In memory of Professor Xunjing Li, Fudan, China, June 3--5, 2005. Hackensack, NJ: World Scientific. 387--395 (2007; Zbl 1196.37115) OpenURL
Wang, Zhi Guo Normal form for families of Hamiltonian systems. (English) Zbl 1126.37041 Acta Math. Sin., Engl. Ser. 23, No. 7, 1199-1216 (2007). MSC: 37J40 PDF BibTeX XML Cite \textit{Z. G. Wang}, Acta Math. Sin., Engl. Ser. 23, No. 7, 1199--1216 (2007; Zbl 1126.37041) Full Text: DOI OpenURL
Hanßmann, Heinz Hamiltonian bifurcations of invariant tori with a vanishing Floquet exponent. (English) Zbl 1107.37043 Dumortier, Freddy (ed.) et al., EQUADIFF 2003. Proceedings of the international conference on differential equations, Hasselt, Belgium, July 22–26, 2003. Hackensack, NJ: World Scientific (ISBN 981-256-169-2/hbk). 732-737 (2005). Reviewer: Messoud A. Efendiev (Berlin) MSC: 37J20 37J40 34C23 PDF BibTeX XML Cite \textit{H. Hanßmann}, in: EQUADIFF 2003. Proceedings of the international conference on differential equations, Hasselt, Belgium, July 22--26, 2003. Hackensack, NJ: World Scientific. 732--737 (2005; Zbl 1107.37043) OpenURL
Dickinson, Detta; Gramchev, Todor; Yoshino, Masafumi Perturbations of vector fields on tori: Resonant normal forms and Diophantine phenomena. (English) Zbl 1032.37010 Proc. Edinb. Math. Soc., II. Ser. 45, No. 3, 731-759 (2002). Reviewer: Veikko Ennola (Turku) MSC: 37C15 11J13 58J40 11J20 35S05 PDF BibTeX XML Cite \textit{D. Dickinson} et al., Proc. Edinb. Math. Soc., II. Ser. 45, No. 3, 731--759 (2002; Zbl 1032.37010) Full Text: DOI OpenURL
Moehlis, Jeff; Knobloch, Edgar Wrinkled tori and bursts due to resonant temporal forcing. (English) Zbl 1020.37030 Physica D 151, No. 2-4, 99-124 (2001). Reviewer: Maria-Christina Ciocci (Gent) MSC: 37G15 37G40 PDF BibTeX XML Cite \textit{J. Moehlis} and \textit{E. Knobloch}, Physica D 151, No. 2--4, 99--124 (2001; Zbl 1020.37030) Full Text: DOI OpenURL
Wei, Baoshe Perturbations of lower dimensional tori in the resonant zone for reversible systems. (English) Zbl 0979.34039 J. Math. Anal. Appl. 253, No. 2, 558-577 (2001). Reviewer: Eugene Ershov (St.Peterburg) MSC: 34D10 93B12 37J40 37J20 37G40 PDF BibTeX XML Cite \textit{B. Wei}, J. Math. Anal. Appl. 253, No. 2, 558--577 (2001; Zbl 0979.34039) Full Text: DOI OpenURL
Stagika, Galina; Ichtiaroglou, Simos Twist and non-twist bifurcations in a system of coupled oscillators. (English) Zbl 0995.70022 Celest. Mech. Dyn. Astron. 78, No. 1-4, 151-160 (2000). MSC: 70K50 PDF BibTeX XML Cite \textit{G. Stagika} and \textit{S. Ichtiaroglou}, Celest. Mech. Dyn. Astron. 78, No. 1--4, 151--160 (2000; Zbl 0995.70022) Full Text: DOI OpenURL
Kunz, Martin Robustness of perturbation series at high energies. (English) Zbl 1005.81027 J. Phys. A, Math. Gen. 33, No. 31, 5567-5597 (2000). MSC: 81Q15 81R12 35B34 37N20 37K55 PDF BibTeX XML Cite \textit{M. Kunz}, J. Phys. A, Math. Gen. 33, No. 31, 5567--5597 (2000; Zbl 1005.81027) Full Text: DOI OpenURL
Rudnev, M.; Wiggins, S. KAM theory near multiplicity one resonant surfaces in perturbations of a priori stable Hamiltonian systems. (English) Zbl 0992.70012 Mechanics: from theory to computation. Essays in honor of Juan-Carlos Simo. Papers invited by Journal of Nonlinear Science editors. New York, NY: Springer. 379-411 (2000). MSC: 70H09 37J40 PDF BibTeX XML Cite \textit{M. Rudnev} and \textit{S. Wiggins}, in: Mechanics: from theory to computation. Essays in honor of Juan-Carlos Simo. Papers invited by Journal of Nonlinear Science editors. New York, NY: Springer. 379--411 (2000; Zbl 0992.70012) OpenURL
Todesco, E.; Gemmi, M. Resonant normal forms for four-dimensional symplectic mappings and applications to nonlinear beam dynamics. (English) Zbl 0979.74034 Simó, Carles (ed.), Hamiltonian systems with three or more degrees of freedom. Proceedings of the NATO Advanced Study Institute, S’Agaró, Spain, June 19-30, 1995. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 533, 600-604 (1999). MSC: 74H55 74H45 37N15 74K10 PDF BibTeX XML Cite \textit{E. Todesco} and \textit{M. Gemmi}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 533, 600--604 (1999; Zbl 0979.74034) OpenURL
Ichtiaroglou, Simos; Meletlidou, Efi The non-integrability of perturbed Hamiltonians of \(N\) degrees of freedom and the continuation of periodic orbits. (English) Zbl 0974.37044 Simó, Carles (ed.), Hamiltonian systems with three or more degrees of freedom. Proceedings of the NATO Advanced Study Institute, S’Agaró, Spain, June 19-30, 1995. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 533, 413-417 (1999). Reviewer: Jörg Härterich (Berlin) MSC: 37J30 70H07 37J40 37-06 PDF BibTeX XML Cite \textit{S. Ichtiaroglou} and \textit{E. Meletlidou}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 533, 413--417 (1999; Zbl 0974.37044) OpenURL
Cheng, Chong-Qing; Wang, Shaoli The surviving of lower dimensional tori from a resonant torus of Hamiltonian systems. (English) Zbl 0936.37029 J. Differ. Equations 155, No. 2, 311-326 (1999). Reviewer: Alexei Ivanov (St.Peterburg) MSC: 37J40 37J35 70H08 PDF BibTeX XML Cite \textit{C.-Q. Cheng} and \textit{S. Wang}, J. Differ. Equations 155, No. 2, 311--326 (1999; Zbl 0936.37029) Full Text: DOI OpenURL
Ichtiaroglou, Simos Non-integrability in Hamiltonian mechanics. (English) Zbl 0884.58045 Celest. Mech. Dyn. Astron. 65, No. 1-2, 21-31 (1997). Reviewer: A.Klíč (Praha) MSC: 37J99 37J40 70H05 PDF BibTeX XML Cite \textit{S. Ichtiaroglou}, Celest. Mech. Dyn. Astron. 65, No. 1--2, 21--31 (1997; Zbl 0884.58045) Full Text: DOI OpenURL
Kozlov, V. V. Symmetries, topology and resonances in Hamiltonian mechanics. Transl. from the Russian by S. V. Bolotin, Y. Fedorov, D. Treshchev. (English) Zbl 0843.58068 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. 31. Berlin: Springer-Verlag. xi, 378 p. (1996). Reviewer: Juan Monterde (Burjasot) MSC: 37J35 37-02 70-02 37J30 37J06 37K10 70H07 70H09 70H33 PDF BibTeX XML Cite \textit{V. V. Kozlov}, Symmetries, topology and resonances in Hamiltonian mechanics. Transl. from the Russian by S. V. Bolotin, Y. Fedorov, D. Treshchev. Berlin: Springer-Verlag (1995; Zbl 0843.58068) OpenURL
Kozlov, V. V. Symmetries, topology and resonances in Hamiltonian mechanics. (Симметрии, топология и резонансы в гамильтоновой механике.) (Russian) Zbl 0921.58029 Izhevsk: Izdatel’stvo Udmurtskogo Universiteta. 429 p. (1995). MSC: 37J35 37K10 37-02 37J99 70H07 70H09 70H33 PDF BibTeX XML Cite \textit{V. V. Kozlov}, Симметрии, топология и резонансы в гамильтоновой механике (Russian). Izhevsk: Izdatel'stvo Udmurt{}skogo Universiteta (1995; Zbl 0921.58029) OpenURL
Bellon, M. P.; Maillard, J. M.; Viallet, C. M. Dynamical systems from quantum integrability. (English) Zbl 0804.58044 Int. J. Mod. Phys. B 7, No. 20-21, 3567-3596 (1993). MSC: 37K35 14E05 82C20 14J50 16W30 PDF BibTeX XML Cite \textit{M. P. Bellon} et al., Int. J. Mod. Phys. B 7, No. 20--21, 3567--3596 (1993; Zbl 0804.58044) Full Text: DOI OpenURL
Gerhard, Ortwin E.; Saha, Prasenjit Recovering galactic orbits by perturbation theory. (English) Zbl 0736.70006 Mon. Not. R. Astron. Soc. 251, No. 3, 449-467 (1991). MSC: 70F15 70H05 37J40 PDF BibTeX XML Cite \textit{O. E. Gerhard} and \textit{P. Saha}, Mon. Not. R. Astron. Soc. 251, No. 3, 449--467 (1991; Zbl 0736.70006) Full Text: DOI OpenURL
Treshchev, D. V. The mechanism of destruction of resonance tori of Hamiltonian systems. (English. Russian original) Zbl 0737.58025 Math. USSR, Sb. 68, No. 1, 181-203 (1990); translation from Mat. Sb. 180, No. 10, 1325-1346 (1989). Reviewer: Yu.Kifer (Jerusalem) MSC: 37J99 37J40 PDF BibTeX XML Cite \textit{D. V. Treshchev}, Math. USSR, Sb. 68, No. 1, 181--203 (1990; Zbl 0737.58025); translation from Mat. Sb. 180, No. 10, 1325--1346 (1989) Full Text: DOI OpenURL
Bolotin, S. V. Motions doubly asymptotic to invariant tori in the theory of perturbed Hamiltonian systems. (English. Russian original) Zbl 0749.70010 J. Appl. Math. Mech. 54, No. 3, 412-417 (1990); translation from Prikl. Mat. Mekh. 54, No. 3, 497-502 (1990). Reviewer: H.Rüßmann (Mainz) MSC: 70H05 37J99 PDF BibTeX XML Cite \textit{S. V. Bolotin}, J. Appl. Math. Mech. 54, No. 3, 412--417 (1990; Zbl 0749.70010); translation from Prikl. Mat. Mekh. 54, No. 3, 497--502 (1990) Full Text: DOI OpenURL
Bovey, J. D.; Dodson, M. M. The Hausdorff dimension of systems of linear forms. (English) Zbl 0534.10025 Acta Arith. 45, 337-358 (1985). MSC: 11J83 11K60 11J13 37J40 PDF BibTeX XML Cite \textit{J. D. Bovey} and \textit{M. M. Dodson}, Acta Arith. 45, 337--358 (1986; Zbl 0534.10025) Full Text: DOI EuDML OpenURL