000149061 001__ 149061 000149061 005__ 20250124153131.0 000149061 0247_ $$2doi$$a10.1103/PhysRevE.84.016701 000149061 0248_ $$2sideral$$a73325 000149061 037__ $$aART-2011-73325 000149061 041__ $$aeng 000149061 100__ $$0(orcid)0000-0002-5692-5876$$aAbad, Alberto$$uUniversidad de Zaragoza 000149061 245__ $$aComputing periodic orbits with arbitrary precision 000149061 260__ $$c2011 000149061 5060_ $$aAccess copy available to the general public$$fUnrestricted 000149061 5203_ $$aThis 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. 000149061 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000149061 590__ $$a2.255$$b2011 000149061 591__ $$aPHYSICS, MATHEMATICAL$$b6 / 55 = 0.109$$c2011$$dQ1$$eT1 000149061 591__ $$aPHYSICS, FLUIDS & PLASMAS$$b10 / 31 = 0.323$$c2011$$dQ2$$eT1 000149061 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000149061 700__ $$0(orcid)0000-0002-8089-343X$$aBarrio, Roberto$$uUniversidad de Zaragoza 000149061 700__ $$0(orcid)0000-0002-1029-0764$$aDena, Angeles 000149061 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000149061 7102_ $$12004$$2398$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física de la Tierra 000149061 773__ $$g84 (2011), 016701 [6 pp.]$$pPhys. rev., E Stat. nonlinear soft matter phys.$$tPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics$$x1539-3755 000149061 8564_ $$s565677$$uhttps://zaguan.unizar.es/record/149061/files/texto_completo.pdf$$yPostprint 000149061 8564_ $$s3107061$$uhttps://zaguan.unizar.es/record/149061/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000149061 909CO $$ooai:zaguan.unizar.es:149061$$particulos$$pdriver 000149061 951__ $$a2025-01-24-14:49:53 000149061 980__ $$aARTICLE