Breden, Maxime; Engel, Maximilian Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems. (English) Zbl 1519.34039 Ann. Appl. Probab. 33, No. 2, 1252-1294 (2023). MSC: 34C28 34F05 34F10 34D08 60H10 60J35 65G99 PDFBibTeX XMLCite \textit{M. Breden} and \textit{M. Engel}, Ann. Appl. Probab. 33, No. 2, 1252--1294 (2023; Zbl 1519.34039) Full Text: DOI arXiv
Lessard, Jean-Philippe; Matsue, Kaname; Takayasu, Akitoshi Saddle-type blow-up solutions with computer-assisted proofs: validation and extraction of global nature. (English) Zbl 1518.34010 J. Nonlinear Sci. 33, No. 3, Paper No. 46, 76 p. (2023). MSC: 34A12 34C11 68V05 PDFBibTeX XMLCite \textit{J.-P. Lessard} et al., J. Nonlinear Sci. 33, No. 3, Paper No. 46, 76 p. (2023; Zbl 1518.34010) Full Text: DOI arXiv
Hill, Dan J.; Bramburger, Jason J.; Lloyd, David J. B. Approximate localised dihedral patterns near a Turing instability. (English) Zbl 1511.35022 Nonlinearity 36, No. 5, 2567-2630 (2023). MSC: 35B32 35B36 35J61 35K57 37L65 34C37 PDFBibTeX XMLCite \textit{D. J. Hill} et al., Nonlinearity 36, No. 5, 2567--2630 (2023; Zbl 1511.35022) Full Text: DOI arXiv
Nitta, Koki; Yamamoto, Nobito; Matsue, Kaname A numerical verification method to specify homoclinic orbits as application of local Lyapunov functions. (English) Zbl 1505.34068 Japan J. Ind. Appl. Math. 39, No. 2, 467-513 (2022). Reviewer: Cristian Vladimirescu (Craiova) MSC: 34C37 34D20 37M21 65G30 PDFBibTeX XMLCite \textit{K. Nitta} et al., Japan J. Ind. Appl. Math. 39, No. 2, 467--513 (2022; Zbl 1505.34068) Full Text: DOI
Constantineau, Kevin; García-Azpeitia, Carlos; Lessard, Jean-Philippe Spatial relative equilibria and periodic solutions of the Coulomb \((n+1)\)-body problem. (English) Zbl 1493.70056 Qual. Theory Dyn. Syst. 21, No. 1, Paper No. 3, 19 p. (2022). MSC: 70F10 65G40 47H11 34C25 37G40 PDFBibTeX XMLCite \textit{K. Constantineau} et al., Qual. Theory Dyn. Syst. 21, No. 1, Paper No. 3, 19 p. (2022; Zbl 1493.70056) Full Text: DOI arXiv
van den Berg, Jan Bouwe; Sheombarsing, Ray Validated computations for connecting orbits in polynomial vector fields. (English) Zbl 1439.34048 Indag. Math., New Ser. 31, No. 2, 310-373 (2020). MSC: 34C37 47N20 34C45 37M99 PDFBibTeX XMLCite \textit{J. B. van den Berg} and \textit{R. Sheombarsing}, Indag. Math., New Ser. 31, No. 2, 310--373 (2020; Zbl 1439.34048) Full Text: DOI arXiv
Alama, Yvonne Bronsard; Lessard, Jean-Philippe Traveling wave oscillatory patterns in a signed Kuramoto-Sivashinsky equation with absorption. (English) Zbl 1432.35039 J. Comput. Appl. Math. 372, Article ID 112608, 7 p. (2020). MSC: 35C07 35K25 35K58 34C25 34C23 34A36 PDFBibTeX XMLCite \textit{Y. B. Alama} and \textit{J.-P. Lessard}, J. Comput. Appl. Math. 372, Article ID 112608, 7 p. (2020; Zbl 1432.35039) Full Text: DOI arXiv
Bánhelyi, Balázs; Csendes, Tibor; Hatvani, László On the existence and stabilization of an upper unstable limit cycle of the damped forced pendulum. (English) Zbl 1447.34042 J. Comput. Appl. Math. 371, Article ID 112702, 9 p. (2020). Reviewer: Oleg Anashkin (Simferopol) MSC: 34C25 34C15 34D20 34H15 70K40 34C28 34H10 PDFBibTeX XMLCite \textit{B. Bánhelyi} et al., J. Comput. Appl. Math. 371, Article ID 112702, 9 p. (2020; Zbl 1447.34042) Full Text: DOI Link
Kepley, Shane; Mireles James, J. D. Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set. (English) Zbl 1451.70033 Celest. Mech. Dyn. Astron. 131, No. 3, Paper No. 13, 55 p. (2019). MSC: 70F15 70K44 34C45 PDFBibTeX XMLCite \textit{S. Kepley} and \textit{J. D. Mireles James}, Celest. Mech. Dyn. Astron. 131, No. 3, Paper No. 13, 55 p. (2019; Zbl 1451.70033) Full Text: DOI
Breden, Maxime; Kuehn, Christian Rigorous validation of stochastic transition paths. (English. French summary) Zbl 1427.60142 J. Math. Pures Appl. (9) 131, 88-129 (2019). Reviewer: Ivan Podvigin (Novosibirsk) MSC: 60H35 65G20 34C45 37C29 37J51 PDFBibTeX XMLCite \textit{M. Breden} and \textit{C. Kuehn}, J. Math. Pures Appl. (9) 131, 88--129 (2019; Zbl 1427.60142) Full Text: DOI arXiv
Castelli, Roberto; Garrione, Maurizio Some unexpected results on the Brillouin singular equation: fold bifurcation of periodic solutions. (English) Zbl 1415.34078 J. Differ. Equations 265, No. 6, 2502-2543 (2018). Reviewer: Alessandro Calamai (Ancona) MSC: 34C25 34B16 37M20 34C23 47N20 PDFBibTeX XMLCite \textit{R. Castelli} and \textit{M. Garrione}, J. Differ. Equations 265, No. 6, 2502--2543 (2018; Zbl 1415.34078) Full Text: DOI
Kalies, William D.; Kepley, Shane; Mireles James, J. D. Analytic continuation of local (un)stable manifolds with rigorous computer assisted error bounds. (English) Zbl 1409.65110 SIAM J. Appl. Dyn. Syst. 17, No. 1, 157-202 (2018). Reviewer: Christian Pötzsche (Klagenfurt) MSC: 65P99 37M99 34C45 PDFBibTeX XMLCite \textit{W. D. Kalies} et al., SIAM J. Appl. Dyn. Syst. 17, No. 1, 157--202 (2018; Zbl 1409.65110) Full Text: DOI arXiv
van den Berg, Jan Bouwe; Breden, Maxime; Lessard, Jean-Philippe; Murray, Maxime Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof. (English) Zbl 1405.34037 J. Differ. Equations 264, No. 5, 3086-3130 (2018). MSC: 34C37 34B40 35C07 34C45 34C14 PDFBibTeX XMLCite \textit{J. B. van den Berg} et al., J. Differ. Equations 264, No. 5, 3086--3130 (2018; Zbl 1405.34037) Full Text: DOI arXiv Link
Mireles-James, J. D. Fourier-Taylor approximation of unstable manifolds for compact maps: numerical implementation and computer-assisted error bounds. (English) Zbl 1383.37066 Found. Comput. Math. 17, No. 6, 1467-1523 (2017). MSC: 37L65 37C05 34C45 37D10 65P40 PDFBibTeX XMLCite \textit{J. D. Mireles-James}, Found. Comput. Math. 17, No. 6, 1467--1523 (2017; Zbl 1383.37066) Full Text: DOI
Capiński, Maciej J.; Mireles James, J. D. Validated computation of heteroclinic sets. (English) Zbl 1418.37125 SIAM J. Appl. Dyn. Syst. 16, No. 1, 375-409 (2017). MSC: 37M25 37C29 34C45 34C05 65L12 65L70 PDFBibTeX XMLCite \textit{M. J. Capiński} and \textit{J. D. Mireles James}, SIAM J. Appl. Dyn. Syst. 16, No. 1, 375--409 (2017; Zbl 1418.37125) Full Text: DOI arXiv
Lessard, Jean-Philippe; Mireles James, J. D.; Ransford, Julian Automatic differentiation for Fourier series and the radii polynomial approach. (English) Zbl 1418.34094 Physica D 334, 174-186 (2016). MSC: 34C25 68W30 PDFBibTeX XMLCite \textit{J.-P. Lessard} et al., Physica D 334, 174--186 (2016; Zbl 1418.34094) Full Text: DOI
Lessard, Jean-Philippe Rigorous verification of saddle-node bifurcations in ODEs. (English) Zbl 1351.34045 Indag. Math., New Ser. 27, No. 4, 1013-1026 (2016). MSC: 34C23 37M20 47N20 PDFBibTeX XMLCite \textit{J.-P. Lessard}, Indag. Math., New Ser. 27, No. 4, 1013--1026 (2016; Zbl 1351.34045) Full Text: DOI
Hungria, Allan; Lessard, Jean-Philippe; Mireles James, J. D. Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach. (English) Zbl 1332.65114 Math. Comput. 85, No. 299, 1427-1459 (2016). MSC: 65L60 65G40 34C25 35K57 PDFBibTeX XMLCite \textit{A. Hungria} et al., Math. Comput. 85, No. 299, 1427--1459 (2016; Zbl 1332.65114) Full Text: DOI Link
D’Ambrosio, Lorenzo; Lessard, Jean-Philippe; Pugliese, Alessandro Blow-up profile for solutions of a fourth order nonlinear equation. (English) Zbl 1325.34045 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 121, 280-335 (2015). Reviewer: Pavel Rehak (Brno) MSC: 34C11 PDFBibTeX XMLCite \textit{L. D'Ambrosio} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 121, 280--335 (2015; Zbl 1325.34045) Full Text: DOI Link
van den Berg, Jan Bouwe; Mireles-James, Jason D.; Lessard, Jean-Philippe; Mischaikow, Konstantin Rigorous numerics for symmetric connecting orbits: even homoclinics of the Gray-Scott equation. (English) Zbl 1231.34081 SIAM J. Math. Anal. 43, No. 4, 1557-1594 (2011). MSC: 34C37 34A45 34B15 47N20 PDFBibTeX XMLCite \textit{J. B. van den Berg} et al., SIAM J. Math. Anal. 43, No. 4, 1557--1594 (2011; Zbl 1231.34081) Full Text: DOI
Haiduc, Radu Horseshoes in the forced van der Pol system. (English) Zbl 1159.37009 Nonlinearity 22, No. 1, 213-237 (2009). Reviewer: Georgy Osipenko (St. Peterburg) MSC: 37D45 34C26 37D20 PDFBibTeX XMLCite \textit{R. Haiduc}, Nonlinearity 22, No. 1, 213--237 (2009; Zbl 1159.37009) Full Text: DOI