149061 20251017144638.0 doi 10.1103/PhysRevE.84.016701 sideral 73325 ART-2011-73325 eng Abad, Alberto Universidad de Zaragoza (orcid)0000-0002-5692-5876 Computing periodic orbits with arbitrary precision 2011 Access copy available to the general public Unrestricted This paper deals with the computation of periodic orbits of dynamical systems up to any arbitrary precision. These very high requirements are useful, for example, in the studies of complex pole location in many physical systems. The algorithm is based on an optimized shooting method combined with a numerical ordinary differential equation (ODE) solver, tides, that uses a Taylor-series method. Nowadays, this methodology is the only one capable of reaching precision up to thousands of digits for ODEs. The method is shown to be quadratically convergent. Some numerical tests for the paradigmatic Lorenz model and the Hénon-Heiles Hamiltonian are presented, giving periodic orbits up to 1000 digits. info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 2.255 2011 PHYSICS, MATHEMATICAL 6 / 55 = 0.109 2011 Q1 T1 PHYSICS, FLUIDS & PLASMAS 10 / 31 = 0.323 2011 Q2 T1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Barrio, Roberto Universidad de Zaragoza (orcid)0000-0002-8089-343X Dena, Angeles (orcid)0000-0002-1029-0764 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 2004 398 Universidad de Zaragoza Dpto. Física Teórica Área Física de la Tierra 84 (2011), 016701 [6 pp.] Phys. rev., E Stat. nonlinear soft matter phys. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 1539-3755 565677 http://zaguan.unizar.es/record/149061/files/texto_completo.pdf Postprint 3107061 http://zaguan.unizar.es/record/149061/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:149061 articulos driver 2025-10-17-14:30:13 ARTICLE