Kumar, Bhanu; Anderson, Rodney L.; de la Llave, Rafael Rapid and accurate methods for computing whiskered tori and their manifolds in periodically perturbed planar circular restricted 3-body problems. (English) Zbl 07467872 Celest. Mech. Dyn. Astron. 134, No. 1, Paper No. 3, 38 p. (2022). Reviewer: Maria Gousidou-Koutita (Thessaloniki) MSC: 70F07 70K43 70F15 PDF BibTeX XML Cite \textit{B. Kumar} et al., Celest. Mech. Dyn. Astron. 134, No. 1, Paper No. 3, 38 p. (2022; Zbl 07467872) Full Text: DOI arXiv OpenURL
de la Llave, Rafael; Xu, Lu Whiskered tori for presymplectic dynamical systems. (English) Zbl 1460.37059 J. Dyn. Differ. Equations 33, No. 1, 1-34 (2021). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37J40 37J38 70K43 53D05 53D22 70H15 PDF BibTeX XML Cite \textit{R. de la Llave} and \textit{L. Xu}, J. Dyn. Differ. Equations 33, No. 1, 1--34 (2021; Zbl 1460.37059) Full Text: DOI OpenURL
Cheng, Hongyu; Si, Wen; Si, Jianguo Whiskered tori for forced beam equations with multi-dimensional Liouvillean frequency. (English) Zbl 1446.37057 J. Dyn. Differ. Equations 32, No. 2, 705-739 (2020). MSC: 37J40 35B25 35L76 35Q56 37L10 35R25 PDF BibTeX XML Cite \textit{H. Cheng} et al., J. Dyn. Differ. Equations 32, No. 2, 705--739 (2020; Zbl 1446.37057) Full Text: DOI OpenURL
Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael Existence of whiskered KAM tori of conformally symplectic systems. (English) Zbl 1471.70017 Nonlinearity 33, No. 1, 538-597 (2020). MSC: 70K43 37J40 70K20 34D35 PDF BibTeX XML Cite \textit{R. C. Calleja} et al., Nonlinearity 33, No. 1, 538--597 (2020; Zbl 1471.70017) Full Text: DOI arXiv OpenURL
Li, Hepeng; Yuan, Xiaoping Quasi-periodic solution for the complex Ginzburg-Landau equation with continuous spectrum. (English) Zbl 1408.35179 J. Math. Phys. 59, No. 11, 112701, 23 p. (2018). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q56 35B15 35P30 70K43 35B35 PDF BibTeX XML Cite \textit{H. Li} and \textit{X. Yuan}, J. Math. Phys. 59, No. 11, 112701, 23 p. (2018; Zbl 1408.35179) Full Text: DOI OpenURL
Capiński, Maciej J.; Zgliczyński, Piotr Beyond the Melnikov method. II: Multidimensional setting. (English) Zbl 1400.37031 J. Differ. Equations 265, No. 9, 3988-4015 (2018). MSC: 37D10 37C29 65G20 PDF BibTeX XML Cite \textit{M. J. Capiński} and \textit{P. Zgliczyński}, J. Differ. Equations 265, No. 9, 3988--4015 (2018; Zbl 1400.37031) Full Text: DOI arXiv OpenURL
Capiński, Maciej J.; Zgliczyński, Piotr Beyond the Melnikov method: A computer assisted approach. (English) Zbl 1368.37035 J. Differ. Equations 262, No. 1, 365-417 (2017). MSC: 37D10 65G20 37M99 70H33 65P40 PDF BibTeX XML Cite \textit{M. J. Capiński} and \textit{P. Zgliczyński}, J. Differ. Equations 262, No. 1, 365--417 (2017; Zbl 1368.37035) Full Text: DOI arXiv OpenURL
Fontich, Ernest; de la Llave, Rafael; Sire, Yannick A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems. (English) Zbl 1237.37040 Electron. Res. Announc. Math. Sci. 16, 9-22 (2009). Reviewer: Pau Martin de la Torre (Barcelona) MSC: 37J40 37K55 37K60 70H08 PDF BibTeX XML Cite \textit{E. Fontich} et al., Electron. Res. Announc. Math. Sci. 16, 9--22 (2009; Zbl 1237.37040) Full Text: DOI OpenURL
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 PDF BibTeX XML Cite \textit{E. Fontich} et al., J. Differ. Equations 246, No. 8, 3136--3213 (2009; Zbl 1209.37066) Full Text: DOI arXiv OpenURL
de la Llave, Rafael Some recent progress in geometric methods in the instability problem in Hamiltonian mechanics. (English) Zbl 1117.37031 Sanz-Solé, Marta (ed.) et al., Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22–30, 2006. Volume II: Invited lectures. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-022-7/hbk). 1705-1729 (2006). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 37J40 37C29 34C37 37C50 34C29 70H08 PDF BibTeX XML Cite \textit{R. de la Llave}, in: Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22--30, 2006. Volume II: Invited lectures. Zürich: European Mathematical Society (EMS). 1705--1729 (2006; Zbl 1117.37031) OpenURL
Procesi, Michela Exponentially small splitting and Arnold diffusion for multiple time scale systems. (English) Zbl 1073.37072 Rev. Math. Phys. 15, No. 4, 339-386 (2003). MSC: 37J40 70H08 37G05 PDF BibTeX XML Cite \textit{M. Procesi}, Rev. Math. Phys. 15, No. 4, 339--386 (2003; Zbl 1073.37072) Full Text: DOI OpenURL
Yagasaki, Kazuyuki Numerical evidence of fast diffusion in a three-degree-of-freedom Hamiltonian system with a saddle-center. (English) Zbl 0997.37035 Phys. Lett., A 301, No. 1-2, 45-52 (2002). MSC: 37J40 70H08 PDF BibTeX XML Cite \textit{K. Yagasaki}, Phys. Lett., A 301, No. 1--2, 45--52 (2002; Zbl 0997.37035) Full Text: DOI OpenURL
Delshams, Amadeu; Gutiérrez, Pere Homoclinic orbits to invariant tori in Hamiltonian systems. (English) Zbl 1140.37355 Jones, Christopher K.R.T. (ed.) et al., Multiple-time-scale dynamical systems. Proceedings of the IMA workshop, Minneapolis, MN, USA, 1997-98. New York, NY: Springer (ISBN 0-387-95126-1/hbk). IMA Vol. Math. Appl. 122, 1-27 (2001). MSC: 37J40 70H08 PDF BibTeX XML Cite \textit{A. Delshams} and \textit{P. Gutiérrez}, IMA Vol. Math. Appl. 122, 1--27 (2001; Zbl 1140.37355) 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
Valdinoci, Enrico Families of whiskered tori for a-priori stable/unstable Hamiltonian systems and construction of unstable orbits. (English) Zbl 0956.37046 Math. Phys. Electron. J. 6, Paper No. 2, 30 p. (2000). MSC: 37J40 37J25 PDF BibTeX XML Cite \textit{E. Valdinoci}, Math. Phys. Electron. J. 6, Paper No.2, 30 p. (2000; Zbl 0956.37046) Full Text: EuDML EMIS OpenURL
Chierchia, Luigi; Valdinoci, Enrico A note on the construction of Hamiltonian trajectories along heteroclinic chains. (English) Zbl 0936.37037 Forum Math. 12, No. 2, 247-255 (2000). Reviewer: J.Andres (Olomouc) MSC: 37J45 37J40 PDF BibTeX XML Cite \textit{L. Chierchia} and \textit{E. Valdinoci}, Forum Math. 12, No. 2, 247--255 (2000; Zbl 0936.37037) Full Text: DOI Link OpenURL
Grote, M. J.; Majda, A. J.; Ragazzo, C. Grotta Dynamic mean flow and small-scale interaction through topographic stress. (English) Zbl 0927.76016 J. Nonlinear Sci. 9, No. 1, 89-130 (1999). MSC: 76B60 76B65 76U05 37N10 86A05 86A10 PDF BibTeX XML Cite \textit{M. J. Grote} et al., J. Nonlinear Sci. 9, No. 1, 89--130 (1999; Zbl 0927.76016) Full Text: DOI OpenURL
Rudnev, Michael; Wiggins, Stephen Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems. (English) Zbl 0941.37021 Physica D 114, No. 1-2, 3-80 (1998). MSC: 37D45 37J45 37C55 34C37 70H05 PDF BibTeX XML Cite \textit{M. Rudnev} and \textit{S. Wiggins}, Physica D 114, No. 1--2, 3--80 (1998; Zbl 0941.37021) Full Text: DOI OpenURL
McLaughlin, David W.; Shatah, Jalal Homoclinic orbits for PDE’s. (English) Zbl 0890.35134 Spigler, Renato et al., Recent advances in partial differential equations, Venice, Italy, June 10–14, 1996. Proceedings of a conference in honor of the 70th birthdays of Peter D. Lax and Louis Nirenberg. Providence, RI: American Mathematical Society. Proc. Symp. Appl. Math. 54, 281-299 (1998). MSC: 35Q53 35Q58 58J72 34C37 PDF BibTeX XML Cite \textit{D. W. McLaughlin} and \textit{J. Shatah}, Proc. Symp. Appl. Math. 54, 281--299 (1998; Zbl 0890.35134) OpenURL
Rudnev, M.; Wiggins, S. KAM theory near multiplicity one resonant surfaces in perturbations of a-priori stable Hamiltonian systems. (English) Zbl 0876.58015 J. Nonlinear Sci. 7, No. 2, 177-209 (1997). MSC: 37J99 37G05 37J35 37K10 37C55 37J40 70H05 70K30 PDF BibTeX XML Cite \textit{M. Rudnev} and \textit{S. Wiggins}, J. Nonlinear Sci. 7, No. 2, 177--209 (1997; Zbl 0876.58015) Full Text: DOI OpenURL
Haller, George; Wiggins, Stephen Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems. (English) Zbl 0894.70014 Physica D 90, No. 3-4, 319-365 (1996). MSC: 70K50 70H05 37D45 PDF BibTeX XML Cite \textit{G. Haller} and \textit{S. Wiggins}, Physica D 90, No. 3--4, 319--365 (1996; Zbl 0894.70014) Full Text: DOI OpenURL
McLaughlin, David W.; Overman, Edward A. II Whiskered tori for integrable PDE’s: Chaotic behavior in near integrable PDE’s. (English) Zbl 0843.35116 Keller, Joseph B. (ed.) et al., Surveys in Applied Mathematics. Vol. 1. New York, NY: Plenum Press. 83-203 (1995). MSC: 35Q55 65Z05 37D45 37J40 PDF BibTeX XML Cite \textit{D. W. McLaughlin} and \textit{E. A. Overman II}, in: Surveys in Applied Mathematics. Vol. 1. New York, NY: Plenum Press. 83--203 (1995; Zbl 0843.35116) OpenURL
McLaughlin, David W. Whiskered tori and chaotic behavior in nonlinear waves. (English) Zbl 0848.58031 Chatterji, S. D. (ed.), Proceedings of the international congress of mathematicians, ICM ’94, August 3-11, 1994, Zürich, Switzerland. Vol. II. Basel: Birkhäuser. 1484-1493 (1995). Reviewer: Li Jibin (Kunming) MSC: 37J35 37K10 35Q55 37E99 PDF BibTeX XML Cite \textit{D. W. McLaughlin}, in: Proceedings of the international congress of mathematicians, ICM '94, August 3-11, 1994, Zürich, Switzerland. Vol. II. Basel: Birkhäuser. 1484--1493 (1995; Zbl 0848.58031) OpenURL
Gentile, Guido Whiskered tori with prefixed frequencies and Lyapunov spectrum. (English) Zbl 0841.58023 Dyn. Stab. Syst. 10, No. 3, 269-308 (1995). MSC: 37J99 70F07 81Q10 PDF BibTeX XML Cite \textit{G. Gentile}, Dyn. Stab. Syst. 10, No. 3, 269--308 (1995; Zbl 0841.58023) Full Text: DOI OpenURL
Gentile, Guido A proof of existence of whiskered tori with quasi flat homoclinic intersections in a class of almost integrable Hamiltonian systems. (English) Zbl 0841.58038 Forum Math. 7, No. 6, 709-753 (1995). Reviewer: M.Farkas (Budapest) MSC: 37C75 34D10 PDF BibTeX XML Cite \textit{G. Gentile}, Forum Math. 7, No. 6, 709--753 (1995; Zbl 0841.58038) Full Text: DOI EuDML OpenURL
Li, Y.; McLaughlin, David W. Morse and Melnikov functions for NLS PDE’s. (English) Zbl 0808.35140 Commun. Math. Phys. 162, No. 1, 175-214 (1994). MSC: 35Q55 35P05 PDF BibTeX XML Cite \textit{Y. Li} and \textit{D. W. McLaughlin}, Commun. Math. Phys. 162, No. 1, 175--214 (1994; Zbl 0808.35140) Full Text: DOI OpenURL
Graham, R.; Tél, T. On the weak-noise limit of Fokker-Planck models. (English) Zbl 0591.60081 J. Stat. Phys. 35, 729-748 (1984). MSC: 60J70 60K35 70F99 PDF BibTeX XML Cite \textit{R. Graham} and \textit{T. Tél}, J. Stat. Phys. 35, 729--748 (1984; Zbl 0591.60081) Full Text: DOI OpenURL