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Topological method for rigorously computing periodic orbits using Fourier modes
1. | Institute for Mathematics, University of Paderborn, D-33095 Paderborn, Germany, Germany, Germany |
[1] |
A. Aschwanden, A. Schulze-Halberg, D. Stoffer. Stable periodic solutions for delay equations with positive feedback - a computer-assisted proof. Discrete and Continuous Dynamical Systems, 2006, 14 (4) : 721-736. doi: 10.3934/dcds.2006.14.721 |
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Piotr Zgliczyński. Steady state bifurcations for the Kuramoto-Sivashinsky equation: A computer assisted proof. Journal of Computational Dynamics, 2015, 2 (1) : 95-142. doi: 10.3934/jcd.2015.2.95 |
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Dietmar Szolnoki. Set oriented methods for computing reachable sets and control sets. Discrete and Continuous Dynamical Systems - B, 2003, 3 (3) : 361-382. doi: 10.3934/dcdsb.2003.3.361 |
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Anete S. Cavalcanti. An existence proof of a symmetric periodic orbit in the octahedral six-body problem. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 1903-1922. doi: 10.3934/dcds.2017080 |
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Chiara Caracciolo, Ugo Locatelli. Computer-assisted estimates for Birkhoff normal forms. Journal of Computational Dynamics, 2020, 7 (2) : 425-460. doi: 10.3934/jcd.2020017 |
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Tatiane C. Batista, Juliano S. Gonschorowski, Fábio A. Tal. Density of the set of endomorphisms with a maximizing measure supported on a periodic orbit. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3315-3326. doi: 10.3934/dcds.2015.35.3315 |
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Maxime Breden, Jean-Philippe Lessard. Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2825-2858. doi: 10.3934/dcdsb.2018164 |
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Thomas Wanner. Computer-assisted equilibrium validation for the diblock copolymer model. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 1075-1107. doi: 10.3934/dcds.2017045 |
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Maciej J. Capiński, Emmanuel Fleurantin, J. D. Mireles James. Computer assisted proofs of two-dimensional attracting invariant tori for ODEs. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 6681-6707. doi: 10.3934/dcds.2020162 |
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István Balázs, Jan Bouwe van den Berg, Julien Courtois, János Dudás, Jean-Philippe Lessard, Anett Vörös-Kiss, JF Williams, Xi Yuan Yin. Computer-assisted proofs for radially symmetric solutions of PDEs. Journal of Computational Dynamics, 2018, 5 (1&2) : 61-80. doi: 10.3934/jcd.2018003 |
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Katja Polotzek, Kathrin Padberg-Gehle, Tobias Jäger. Set-oriented numerical computation of rotation sets. Journal of Computational Dynamics, 2017, 4 (1&2) : 119-141. doi: 10.3934/jcd.2017004 |
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Andrea Venturelli. A Variational proof of the existence of Von Schubart's orbit. Discrete and Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 699-717. doi: 10.3934/dcdsb.2008.10.699 |
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Lorenzo Valvo, Ugo Locatelli. Hamiltonian control of magnetic field lines: Computer assisted results proving the existence of KAM barriers. Journal of Computational Dynamics, 2022 doi: 10.3934/jcd.2022002 |
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Wade Hindes. Orbit counting in polarized dynamical systems. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 189-210. doi: 10.3934/dcds.2021112 |
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Tim Austin. A new dynamical proof of the Shmerkin–Wu theorem. Journal of Modern Dynamics, 2022, 18: 1-11. doi: 10.3934/jmd.2022001 |
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Ugo Locatelli, Letizia Stefanelli. Quasi-periodic motions in a special class of dynamical equations with dissipative effects: A pair of detection methods. Discrete and Continuous Dynamical Systems - B, 2015, 20 (4) : 1155-1187. doi: 10.3934/dcdsb.2015.20.1155 |
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Shi-Liang Wu, Cheng-Hsiung Hsu. Entire solutions with merging fronts to a bistable periodic lattice dynamical system. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 2329-2346. doi: 10.3934/dcds.2016.36.2329 |
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Jong-Shenq Guo, Chang-Hong Wu. Front propagation for a two-dimensional periodic monostable lattice dynamical system. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 197-223. doi: 10.3934/dcds.2010.26.197 |
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Peter Giesl. Converse theorem on a global contraction metric for a periodic orbit. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 5339-5363. doi: 10.3934/dcds.2019218 |
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Minju Lee, Hee Oh. Topological proof of Benoist-Quint's orbit closure theorem for $ \boldsymbol{ \operatorname{SO}(d, 1)} $. Journal of Modern Dynamics, 2019, 15: 263-276. doi: 10.3934/jmd.2019021 |
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