A database of rigorous and high-precision periodic orbits of the Lorenz model. A benchmark database of very high-precision numerical and validated initial conditions of periodic orbits for the Lorenz model is presented. This database is a “computational challenge” and it provides the initial conditions of all periodic orbits of the Lorenz model up to multiplicity 10 and guarantees their existence via computer-assisted proofs methods. The orbits are computed using high-precision arithmetic and mixing several techniques resulting in 1000 digits of precision on the initial conditions of the periodic orbits, and intervals of size 10100 that prove the existence of each orbit.
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References in zbMATH (referenced in 6 articles )
Showing results 1 to 6 of 6.
- van den Berg, Jan Bouwe; Sheombarsing, Ray: Rigorous numerics for ODEs using Chebyshev series and domain decomposition (2021)
- Creaser, Jennifer L.; Krauskopf, Bernd; Osinga, Hinke M.: Finding first foliation tangencies in the Lorenz system (2017)
- Wilczak, Daniel; Barrio, Roberto: Systematic computer-assisted proof of branches of stable elliptic periodic orbits and surrounding invariant tori (2017)
- Gilmore, Robert; Rosalie, Martin: Algorithms for concatenating templates (2016)
- Wilczak, Daniel; Serrano, Sergio; Barrio, Roberto: Coexistence and dynamical connections between hyperchaos and chaos in the 4D Rössler system: a computer-assisted proof (2016)
- Barrio, Roberto; Dena, Angeles; Tucker, Warwick: A database of rigorous and high-precision periodic orbits of the Lorenz model (2015)