Zhang, Xiaoming; Li, Denghui; Liu, Xianbin Time-dependent billiards, variational method, and invariant tori. (English) Zbl 07972415 Nonlinearity 38, No. 2, Article ID 025003, 24 p., 24 p. (2025). MSC: 37J40 70F99 70H30 × Cite Format Result Cite Review PDF Full Text: DOI
Corsi, Livia; Gentile, Guido; Procesi, Michela Maximal tori in infinite-dimensional Hamiltonian systems: a renormalisation group approach. (English) Zbl 07920610 Regul. Chaotic Dyn. 29, No. 4, 677-715 (2024). MSC: 37K55 37J40 70H08 70K43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hu, Shengqing; Zhang, Jing Response solutions for finite smooth harmonic oscillators with quasi-periodic forcing. (English) Zbl 1541.37064 Discrete Contin. Dyn. Syst. 44, No. 5, 1267-1286 (2024). MSC: 37J40 70K43 70K40 70K60 34C15 70H08 70H09 34C27 × Cite Format Result Cite Review PDF Full Text: DOI
Si, Wen; Xu, Lu; Yi, Yingfei Response solutions in singularly perturbed, quasi-periodically forced nonlinear oscillators. (English) Zbl 1530.34040 J. Nonlinear Sci. 33, No. 6, Paper No. 114, 28 p. (2023). Reviewer: Michal Veselý (Brno) MSC: 34C27 34E15 37C60 34D20 34E10 × Cite Format Result Cite Review PDF Full Text: DOI
Burby, J. W.; MacKay, R. S.; Naik, S. Isodrastic magnetic fields for suppressing transitions in guiding-centre motion. (English) Zbl 1538.78007 Nonlinearity 36, No. 11, 5884-5954 (2023). MSC: 78A35 82D75 82D10 37J46 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ge, Chuanfang; Geng, Jiansheng; Yi, Yingfei Quasi-periodic breathers in granular chains with Hertzian contact potential. (English) Zbl 1527.37081 J. Nonlinear Sci. 33, No. 5, Paper No. 93, 28 p. (2023). MSC: 37K60 37K55 37J40 34C15 70K43 × Cite Format Result Cite Review PDF Full Text: DOI
Hu, Shengqing Quasi-periodic solutions for Schrödinger equation with finite smooth quasi-periodic forcing. (English) Zbl 1522.35468 SIAM J. Appl. Dyn. Syst. 22, No. 3, 1945-1982 (2023). MSC: 35Q55 70H08 70H12 37J40 35B65 × Cite Format Result Cite Review PDF Full Text: DOI
Chen, Qinbo; Damjanović, Danijela Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus. (English) Zbl 1539.37036 Trans. Am. Math. Soc. 376, No. 6, 4043-4083 (2023). MSC: 37C85 37C15 37C20 37D30 37J40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bustamante, Adrián P.; Chandre, Cristel Numerical computation of critical surfaces for the breakup of invariant tori in Hamiltonian systems. (English) Zbl 1515.37096 SIAM J. Appl. Dyn. Syst. 22, No. 1, 483-500 (2023). MSC: 37M21 37J40 37C55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chierchia, Luigi; Procesi, Michela Kolmogorov-Arnold-Moser (KAM) theory for finite and infinite dimensional systems. (English) Zbl 1548.37007 Gaeta, Giuseppe (ed.), Perturbation theory. Mathematics, methods and applications. New York, NY: Springer; Springer Reference. Encycl. Complex. Syst. Sci. Ser., 247-289 (2022). MSC: 37-02 37K55 37J40 35B20 35B25 70K55 × Cite Format Result Cite Review PDF Full Text: DOI
Ge, Chuanfang; Geng, Jiansheng; Yi, Yingfei Quasi-periodic breathers in Newton’s cradle. (English) Zbl 1509.37106 J. Math. Phys. 63, No. 8, Article ID 082703, 21 p. (2022). MSC: 37K60 37K55 37J40 × Cite Format Result Cite Review PDF Full Text: DOI
Shelukhin, Egor Viterbo conjecture for Zoll symmetric spaces. (English) Zbl 1547.53096 Invent. Math. 230, No. 1, 321-373 (2022). Reviewer: Jean-Philippe Chassé (Zürich) MSC: 53D12 53C35 57R17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Qinbo; Damjanović, Danijela; Petković, Boris On simultaneous linearization of certain commuting nearly integrable diffeomorphisms of the cylinder. (English) Zbl 1528.37038 Math. Z. 301, No. 2, 1881-1912 (2022). MSC: 37E40 37C05 37J35 37J40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Jing, Tianqi; Si, Wen Moser’s theorem for hyperbolic-type degenerate lower tori in Hamiltonian system. (English) Zbl 1483.37080 J. Differ. Equations 299, 602-629 (2021). Reviewer: Stefano Marò (Pisa) MSC: 37J40 70H08 70K43 × Cite Format Result Cite Review PDF Full Text: DOI
Jian, Wenwen Reducibility of the quantum harmonic oscillator in \(d\)-dimensions with finitely differentiable perturbations. (English) Zbl 1454.81066 J. Math. Phys. 61, No. 8, 082701, 34 p. (2020). MSC: 81Q05 35J10 35B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Jing Reducibility for Schrödinger operator with finite smooth and time-quasi-periodic potential. (English) Zbl 1440.35222 Chin. Ann. Math., Ser. B 41, No. 3, 419-440 (2020). Reviewer: Michael Perelmuter (Kyïv) MSC: 35P05 37K55 81Q15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Jing Reducibility, Lyapunov exponent, pure point spectra property for quasi-periodic wave operator. (English) Zbl 1440.37069 Taiwanese J. Math. 24, No. 2, 377-411 (2020). MSC: 37K55 35P05 35L05 81Q15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Sun, Yingte; Li, Jing; Xie, Bing Reducibility for wave equations of finitely smooth potential with periodic boundary conditions. (English) Zbl 1454.35010 J. Differ. Equations 266, No. 5, 2762-2804 (2019). Reviewer: Dimitar A. Kolev (Sofia) MSC: 35A22 37K55 81Q15 35L20 35B15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liang, Zhenguo; Wang, Zhiguo Reducibility of quantum harmonic oscillator on \(\mathbb{R}^d\) with differential and quasi-periodic in time potential. (English) Zbl 1430.35170 J. Differ. Equations 267, No. 5, 3355-3395 (2019). Reviewer: Christian Seifert (Hamburg) MSC: 35P05 37K55 81Q15 35Q41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shen, Jianhua; Chen, Lu; Yuan, Xiaoping Lagrange stability for impulsive Duffing equations. (English) Zbl 1416.34023 J. Differ. Equations 266, No. 11, 6924-6962 (2019). Reviewer: Anatoly Martynyuk (Kyïv) MSC: 34C11 34A37 37C27 34C15 37J40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Villanueva, Jordi A parameterization method for Lagrangian tori of exact symplectic maps of \(\mathbb{R}^{2r}\). (English) Zbl 1408.37093 SIAM J. Appl. Dyn. Syst. 17, No. 3, 2289-2331 (2018). MSC: 37J10 37J40 70K43 × Cite Format Result Cite Review PDF Full Text: DOI Link
Villanueva, Jordi A new approach to the parameterization method for Lagrangian tori of Hamiltonian systems. (English) Zbl 1456.37067 J. Nonlinear Sci. 27, No. 2, 495-530 (2017). MSC: 37J40 70K43 70H08 × Cite Format Result Cite Review PDF Full Text: DOI Link
Yuan, Xiaoping Boundedness of solutions for Duffing equation with low regularity in time. (English) Zbl 1394.34063 Chin. Ann. Math., Ser. B 38, No. 5, 1037-1046 (2017). Reviewer: Zaihong Wang (Beijing) MSC: 34C11 34D20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Figueras, J.-Ll.; Haro, A.; Luque, A. Rigorous computer-assisted application of KAM theory: a modern approach. (English) Zbl 1383.37047 Found. Comput. Math. 17, No. 5, 1123-1193 (2017). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 37J40 37J10 65G20 65G40 65T50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Gao, Meina; Zhang, Kangkang Quasi-periodic solutions for the derivative nonlinear Schrödinger equation with finitely differentiable nonlinearities. (English) Zbl 1367.37056 Chin. Ann. Math., Ser. B 38, No. 3, 759-786 (2017). MSC: 37K55 35B15 35J10 35Q40 35Q55 × Cite Format Result Cite Review PDF Full Text: DOI
Bernard, Patrick; Kaloshin, Vadim; Zhang, Ke Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. (English) Zbl 1368.37068 Acta Math. 217, No. 1, 1-79 (2016). Reviewer: William J. Satzer Jr. (St. Paul) MSC: 37J40 37J45 70H08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Berti, Massimiliano; Bolle, Philippe A Nash-Moser approach to KAM theory. (English) Zbl 1342.37073 Guyenne, Philippe (ed.) et al., Hamiltonian partial differential equations and applications. Selected papers based on the presentations at the conference on Hamiltonian PDEs: analysis, computations and applications, Toronto, Canada, January 10–12, 2014. Toronto: The Fields Institute for Research in the Mathematical Sciences; New York, NY: Springer (ISBN 978-1-4939-2949-8/hbk; 978-1-4939-2950-4/ebook). Fields Institute Communications 75, 255-284 (2015). Reviewer: Christopher Policastro (Berkeley) MSC: 37K55 × Cite Format Result Cite Review PDF Full Text: DOI
Mramor, Blaž; Rink, Bob Continuity of the Peierls barrier and robustness of laminations. (English) Zbl 1364.37135 Ergodic Theory Dyn. Syst. 35, No. 4, 1263-1288 (2015). Reviewer: Dongfeng Zhang (Nanjing) MSC: 37J45 37J40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mramor, Blaž; Rink, Bob A dichotomy theorem for minimizers of monotone recurrence relations. (English) Zbl 1321.37063 Ergodic Theory Dyn. Syst. 35, No. 1, 215-248 (2015). Reviewer: William J. Satzer jun. (St. Paul) MSC: 37J50 37E40 70H30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
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 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Liang, Zhenguo; Yan, Jun; Yi, Yingfei Viscous stability of quasi-periodic tori. (English) Zbl 1418.37043 Ergodic Theory Dyn. Syst. 34, No. 1, 185-210 (2014). MSC: 37C40 37J50 37J40 × Cite Format Result Cite Review PDF Full Text: DOI
Yuan, Xiaoping; Zhang, Kangkang A reduction theorem for time dependent Schrödinger operator with finite differentiable unbounded perturbation. (English) Zbl 1282.81086 J. Math. Phys. 54, No. 5, 052701, 23 p. (2013). MSC: 81Q05 35Q41 81R12 35B20 35B35 × Cite Format Result Cite Review PDF Full Text: DOI
Bessi, Ugo The Aubry set for a version of the Vlasov equation. (English) Zbl 1350.37069 NoDEA, Nonlinear Differ. Equ. Appl. 20, No. 4, 1411-1452 (2013). Reviewer: Mario Jorge Dias Carneiro (Belo Horizonte) MSC: 37J50 35Q83 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Su, Xifeng; Wang, Lin Total destruction of invariant tori for the generalized Frenkel-Kontorova model. (English) Zbl 1274.82064 J. Math. Phys. 53, No. 2, 022702, 7 p. (2012). MSC: 82D20 82D25 82D30 70K43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Su, Xifeng; de la Llave, Rafael Percival Lagrangian approach to the Aubry-Mather theory. (English) Zbl 1337.70037 Expo. Math. 30, No. 2, 182-208 (2012). MSC: 70H12 37J50 37J45 39A14 49J40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Corsi, Livia; Gentile, Guido; Procesi, Michela KAM theory in configuration space and cancellations in the Lindstedt series. (English) Zbl 1238.37017 Commun. Math. Phys. 302, No. 2, 359-402 (2011). Reviewer: Vassilios Rothos (Thessaloniki) MSC: 37J40 70H08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Calleja, Renato; Celletti, Alessandra Breakdown of invariant attractors for the dissipative standard map. (English) Zbl 1311.37068 Chaos 20, No. 1, 013121, 9 p. (2010). MSC: 37M20 37B25 34D45 37J40 × Cite Format Result Cite Review PDF Full Text: DOI Link
Calleja, Renato; de la Llave, Rafael Computation of the breakdown of analyticity in statistical mechanics models: Numerical results and a renormalization group explanation. (English) Zbl 1205.82067 J. Stat. Phys. 141, No. 6, 940-951 (2010). MSC: 82B26 82B27 82B28 82-08 × Cite Format Result Cite Review PDF Full Text: DOI
Bounemoura, Abed Nekhoroshev estimates for finitely differentiable quasi-convex Hamiltonians. (English) Zbl 1206.37029 J. Differ. Equations 249, No. 11, 2905-2920 (2010). Reviewer: Igor Andrianov (Köln) MSC: 37J40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Berti, M.; Bolle, P.; Procesi, M. An abstract Nash-Moser theorem with parameters and applications to PDEs. (English) Zbl 1203.47038 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 27, No. 1, 377-399 (2010). Reviewer: Lutz Recke (Berlin) MSC: 47J07 47N20 × Cite Format Result Cite Review PDF Full Text: DOI
Liang, Zhenguo; Yan, Jun Strong stability of KAM tori: From the point of view of viscosity solutions of H-J equations. (English) Zbl 1196.35046 J. Dyn. Differ. Equations 21, No. 2, 353-370 (2009). MSC: 35B35 35F25 37K55 × Cite Format Result Cite Review PDF Full Text: DOI
Fontich, Ernest; de la Llave, Rafael; Sire, Yannick Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions. (English) Zbl 1209.37066 J. Differ. Equations 246, No. 8, 3136-3213 (2009). Reviewer: Maria Saprykina (Stockholm) MSC: 37J40 37D05 70H08 70K43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhang, Jing On lower dimensional invariant tori in \(C^d\) reversible systems. (English) Zbl 1154.37359 Chin. Ann. Math., Ser. B 29, No. 5, 459-486 (2008). MSC: 37J40 37C55 × Cite Format Result Cite Review PDF Full Text: DOI
González-Enríquez, A.; de la Llave, R. Analytic smoothing of geometric maps with applications to KAM theory. (English) Zbl 1160.37024 J. Differ. Equations 245, No. 5, 1243-1298 (2008). Reviewer: Xiaoping Yuan (Shanghai) MSC: 37J40 37J10 × Cite Format Result Cite Review PDF Full Text: DOI
González-Enríquez, A.; Vano, J. An estimate of smoothing and composition with applications to conjugation problems. (English) Zbl 1148.26019 J. Dyn. Differ. Equations 20, No. 1, 239-270 (2008). Reviewer: Vladimir V. Peller (East Lansing) MSC: 26D10 37C05 41A35 × Cite Format Result Cite Review PDF Full Text: DOI
Bourgain, Jean; Kaloshin, Vadim On diffusion in high-dimensional Hamiltonian systems. (English) Zbl 1080.37062 J. Funct. Anal. 229, No. 1, 1-61 (2005). MSC: 37J40 37J45 37J15 × Cite Format Result Cite Review PDF Full Text: DOI
Cheng, Chong-Qing Minimal invariant tori in the resonant regions for nearly integrable Hamiltonian systems. (English) Zbl 1073.37071 Trans. Am. Math. Soc. 357, No. 12, 5067-5095 (2005). MSC: 37J40 37J50 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Yong; Yi, Yingfei Persistence of hyperbolic tori in Hamiltonian systems. (English) Zbl 1060.37045 J. Differ. Equations 208, No. 2, 344-387 (2005). MSC: 37J40 × Cite Format Result Cite Review PDF Full Text: DOI Link
Chierchia, Luigi; Qian, Dingbian Moser’s theorem for lower dimensional tori. (English) Zbl 1144.37444 J. Differ. Equations 206, No. 1, 55-93 (2004). MSC: 37J40 34C27 70H08 × Cite Format Result Cite Review PDF Full Text: DOI
Mora, Leonardo; Romero, Neptalí Persistence of homoclinic tangencies for area-preserving maps. (English) Zbl 0932.37033 Ann. Fac. Sci. Toulouse, VI. Sér., Math. 6, No. 4, 711-725 (1997). MSC: 37G25 37E35 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Chierchia, L.; Falcolini, C. Compensations in small divisor problems. (English) Zbl 0847.58026 Commun. Math. Phys. 175, No. 1, 135-160 (1996). MSC: 37J99 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Berretti, Alberto; Marmi, Stefano Scaling, perturbative renormalization and analyticity for the standard map and some generalizations. (English) Zbl 0817.58014 Chaos Solitons Fractals 5, No. 2, 257-269 (1995). MSC: 37J99 81T15 37J40 × Cite Format Result Cite Review PDF Full Text: DOI
Forni, Giovanni Analytic destruction of invariant circles. (English) Zbl 0817.58018 Ergodic Theory Dyn. Syst. 14, No. 2, 267-298 (1994). Reviewer: R.Cowen (Nairobi) MSC: 37A99 37J35 37K10 × Cite Format Result Cite Review PDF Full Text: DOI
Popov, Georgi S. Length spectrum invariants of Riemannian manifolds. (English) Zbl 0804.53068 Math. Z. 213, No. 2, 311-351 (1993). Reviewer: A.P.Stone (Albuquerque) MSC: 53C22 53C20 58J50 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Falcolini, Corrado; de la Llave, R. A rigorous partial justification of Greene’s criterion. (English) Zbl 0892.58045 J. Stat. Phys. 67, No. 3-4, 609-643 (1992). MSC: 37C75 × Cite Format Result Cite Review PDF Full Text: DOI
Ito, Hidekazu Action-angle coordinates at singularities for analytic integrable systems. (English) Zbl 0707.58026 Math. Z. 206, No. 3, 363-407 (1991). Reviewer: H.Ito MSC: 37J35 37K10 37J99 37G05 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Mather, John N. Action minimizing invariant measures for positive definite Lagrangian systems. (English) Zbl 0696.58027 Math. Z. 207, No. 2, 169-207 (1991). Reviewer: J.N.Mather MSC: 37J50 37C10 37J40 37E40 28D20 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Levi, Mark Quasiperiodic motions in superquadratic time-periodic potentials. (English) Zbl 0744.34043 Commun. Math. Phys. 143, No. 1, 43-83 (1991). Reviewer: Y.Kivshar (Düsseldorf) MSC: 34C27 70K30 34C20 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Chierchia, Luigi A direct method for constructing solutions of the Hamilton-Jacobi equation. (English) Zbl 0726.70009 Meccanica 25, No. 4, 246-252 (1990). Reviewer: Á.Bosznay (Budapest) MSC: 70H20 70-08 × Cite Format Result Cite Review PDF Full Text: DOI
Celletti, Alessandra Analysis of resonances in the spin-orbit problem in celestial mechanics. II: Higher order resonances and some numerical experiments. (English) Zbl 0711.70016 Z. Angew. Math. Phys. 41, No. 4, 453-479 (1990). MSC: 70F15 70K30 × Cite Format Result Cite Review PDF Full Text: DOI
Pöschel, Jürgen Small divisors with spatial structure in infinite dimensional Hamiltonian systems. (English) Zbl 0702.58065 Commun. Math. Phys. 127, No. 2, 351-393 (1990). MSC: 37J40 37J99 37J35 37K10 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Celletti, Alessandra Analysis of resonances in the spin-orbit problem in celestial mechanics. I: The synchronous resonance. (English) Zbl 0699.70014 Z. Angew. Math. Phys. 41, No. 2, 174-204 (1990). MSC: 70F15 70K20 70M20 70-08 × Cite Format Result Cite Review PDF Full Text: DOI
Herman, Michael R. Inégalités “a priori” pour des tores lagrangiens invariants par des difféomorphismes symplectiques. (‘A priori’ inequalities for Langrangian tori invariant under symplectic diffeomorphisms). (French) Zbl 0717.58020 Publ. Math., Inst. Hautes Étud. Sci. 70, 47-101 (1989). Reviewer: D.Nguyen Huu MSC: 37J99 37J35 37K10 37C80 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
MacKay, R. S. A criterion for non-existence of invariant tori for Hamiltonian systems. (English) Zbl 0699.58029 Physica D 36, No. 1-2, 64-82 (1989). Reviewer: M.Baake MSC: 37J99 37C80 × Cite Format Result Cite Review PDF Full Text: DOI
Chierchia, L.; Zehnder, E. Asymptotic expansions of quasiperiodic solutions. (English) Zbl 0695.34040 Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 16, No. 2, 245-258 (1989). Reviewer: L.Chierchia MSC: 34C27 35C20 34C15 37-XX 34D30 30B10 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML
Pöschel, Jürgen On elliptic lower dimensional tori in Hamiltonian systems. (English) Zbl 0662.58037 Math. Z. 202, No. 4, 559-608 (1989). Reviewer: Jürgen Pöschel (Bonn) MSC: 37J40 37J99 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Celletti, Alessandra; Chierchia, Luigi Construction of analytic KAM-surfaces and effective stability bounds. (English) Zbl 0657.58032 Commun. Math. Phys. 118, No. 1, 119-161 (1988). Reviewer: A.Givental’ MSC: 37J40 37C55 70H15 × Cite Format Result Cite Review PDF Full Text: DOI Euclid