Calleja, Renato; Celletti, Alessandra; Gimeno, Joan; de la Llave, Rafael Accurate computations up to breakdown of quasi-periodic attractors in the dissipative spin-orbit problem. (English) Zbl 07776676 J. Nonlinear Sci. 34, No. 1, Paper No. 12, 38 p. (2024). MSC: 70F15 70H08 70H12 70-08 PDFBibTeX XMLCite \textit{R. Calleja} et al., J. Nonlinear Sci. 34, No. 1, Paper No. 12, 38 p. (2024; Zbl 07776676) Full Text: DOI arXiv OA License
Duignan, Nathan; Meiss, James D. Distinguishing between regular and chaotic orbits of flows by the weighted Birkhoff average. (English) Zbl 1520.37048 Physica D 449, Article ID 133749, 16 p. (2023). MSC: 37J40 37J35 37A30 70K55 37E45 PDFBibTeX XMLCite \textit{N. Duignan} and \textit{J. D. Meiss}, Physica D 449, Article ID 133749, 16 p. (2023; Zbl 1520.37048) Full Text: DOI arXiv
Das, Suddhasattwa Lie group valued Koopman eigenfunctions. (English) Zbl 1511.22011 Nonlinearity 36, No. 5, 2149-2165 (2023). MSC: 22E15 22E60 37C15 37C85 PDFBibTeX XMLCite \textit{S. Das}, Nonlinearity 36, No. 5, 2149--2165 (2023; Zbl 1511.22011) Full Text: DOI arXiv
González, Alejandra; Haro, Àlex; de la Llave, Rafael Efficient and reliable algorithms for the computation of non-twist invariant circles. (English) Zbl 1501.37064 Found. Comput. Math. 22, No. 3, 791-847 (2022). MSC: 37J40 37J20 37M20 65T50 PDFBibTeX XMLCite \textit{A. González} et al., Found. Comput. Math. 22, No. 3, 791--847 (2022; Zbl 1501.37064) Full Text: DOI
Sales, Matheus R.; Mugnaine, Michele; Viana, Ricardo L.; Caldas, Iberê L.; Szezech, José D. Unpredictability in Hamiltonian systems with a hierarchical phase space. (English) Zbl 1486.81120 Phys. Lett., A 431, Article ID 127991, 7 p. (2022). MSC: 81Q50 70H05 35G20 70M20 90C70 PDFBibTeX XMLCite \textit{M. R. Sales} et al., Phys. Lett., A 431, Article ID 127991, 7 p. (2022; Zbl 1486.81120) Full Text: DOI
Calleja, Renato; Celletti, Alessandra; Gimeno, Joan; de la Llave, Rafael Efficient and accurate KAM tori construction for the dissipative spin-orbit problem using a map reduction. (English) Zbl 1505.70035 J. Nonlinear Sci. 32, No. 1, Paper No. 4, 40 p. (2022). MSC: 70F15 70K43 70H08 70-08 37N05 PDFBibTeX XMLCite \textit{R. Calleja} et al., J. Nonlinear Sci. 32, No. 1, Paper No. 4, 40 p. (2022; Zbl 1505.70035) Full Text: DOI arXiv
Calleja, Renato; Celletti, Alessandra; Gimeno, Joan; de la Llave, Rafael KAM quasi-periodic tori for the dissipative spin-orbit problem. (English) Zbl 1480.37070 Commun. Nonlinear Sci. Numer. Simul. 106, Article ID 106099, 22 p. (2022). MSC: 37J40 37C70 37M22 37N05 70H08 70F15 PDFBibTeX XMLCite \textit{R. Calleja} et al., Commun. Nonlinear Sci. Numer. Simul. 106, Article ID 106099, 22 p. (2022; Zbl 1480.37070) Full Text: DOI arXiv
Meiss, J. D.; Sander, E. Birkhoff averages and the breakdown of invariant tori in volume-preserving maps. (English) Zbl 1491.37076 Physica D 428, Article ID 133048, 20 p. (2021). MSC: 37M25 37M21 37A30 37A05 37J40 PDFBibTeX XMLCite \textit{J. D. Meiss} and \textit{E. Sander}, Physica D 428, Article ID 133048, 20 p. (2021; Zbl 1491.37076) Full Text: DOI arXiv
Sander, E.; Meiss, J. D. Birkhoff averages and rotational invariant circles for area-preserving maps. (English) Zbl 1496.37063 Physica D 411, Article ID 132569, 19 p. (2020). MSC: 37J40 37E45 37A30 37A05 PDFBibTeX XMLCite \textit{E. Sander} and \textit{J. D. Meiss}, Physica D 411, Article ID 132569, 19 p. (2020; Zbl 1496.37063) Full Text: DOI arXiv
Figueras, Jordi-Lluís; Haro, Alex; Luque, Alejandro Effective bounds for the measure of rotations. (English) Zbl 1436.37052 Nonlinearity 33, No. 2, 700-741 (2020). Reviewer: Abderrazek Benhassine (Monastir) MSC: 37E10 37E45 37J40 PDFBibTeX XMLCite \textit{J.-L. Figueras} et al., Nonlinearity 33, No. 2, 700--741 (2020; Zbl 1436.37052) Full Text: DOI arXiv
Tao, Molei Simply improved averaging for coupled oscillators and weakly nonlinear waves. (English) Zbl 1466.70025 Commun. Nonlinear Sci. Numer. Simul. 71, 1-21 (2019). MSC: 70K65 34C15 34C29 PDFBibTeX XMLCite \textit{M. Tao}, Commun. Nonlinear Sci. Numer. Simul. 71, 1--21 (2019; Zbl 1466.70025) Full Text: DOI arXiv
Das, Suddhasattwa; Saiki, Yoshitaka; Sander, Evelyn; Yorke, James A. Solving the Babylonian problem of quasiperiodic rotation rates. (English) Zbl 1441.37094 Discrete Contin. Dyn. Syst., Ser. S 12, No. 8, 2279-2305 (2019). MSC: 37N05 37A30 37C55 70F07 70H12 70K43 PDFBibTeX XMLCite \textit{S. Das} et al., Discrete Contin. Dyn. Syst., Ser. S 12, No. 8, 2279--2305 (2019; Zbl 1441.37094) Full Text: DOI arXiv
Saiki, Yoshitaka; Yorke, James A. Quasi-periodic orbits in Siegel disks/balls and the Babylonian problem. (English) Zbl 1412.37052 Regul. Chaotic Dyn. 23, No. 6, 735-750 (2018). MSC: 37F50 37C55 37A30 PDFBibTeX XMLCite \textit{Y. Saiki} and \textit{J. A. Yorke}, Regul. Chaotic Dyn. 23, No. 6, 735--750 (2018; Zbl 1412.37052) Full Text: DOI arXiv
Salahshoor, Hossein; de la Llave, Rafael A numerical investigation of the pinning phenomenon in quasi-periodic Frenkel Kontorova model under an external force. (A numerical investigation of the pinning phenomenon in quasi-periodic Frenkel Kontrova model under an external force.) (English) Zbl 1404.82038 J. Stat. Phys. 173, No. 2, 398-410 (2018). MSC: 82C20 82D25 82C80 65C05 PDFBibTeX XMLCite \textit{H. Salahshoor} and \textit{R. de la Llave}, J. Stat. Phys. 173, No. 2, 398--410 (2018; Zbl 1404.82038) Full Text: DOI
Das, Suddhasattwa; Yorke, James A. Super convergence of ergodic averages for quasiperiodic orbits. (English) Zbl 1384.37010 Nonlinearity 31, No. 2, 491-501 (2018). Reviewer: Hasan Akin (Gaziantep) MSC: 37A30 37A25 37A05 37A45 PDFBibTeX XMLCite \textit{S. Das} and \textit{J. A. Yorke}, Nonlinearity 31, No. 2, 491--501 (2018; Zbl 1384.37010) Full Text: DOI arXiv
Kamiyama, Kyohei; Komuro, Motomasa; Aihara, Kazuyuki Homoclinic cycle bifurcations in planar maps. (English) Zbl 1360.37128 Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 3, Article ID 1730012, 11 p. (2017). MSC: 37G20 37E30 37D45 37G25 PDFBibTeX XMLCite \textit{K. Kamiyama} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 3, Article ID 1730012, 11 p. (2017; Zbl 1360.37128) Full Text: DOI