title: Computing periodic orbits with arbitrary precision.
abstract: 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.
authors.affiliation: Department of Theoretical Physics and IUMA, University of Zaragoza, Zaragoza, Spain. abad@unizar.es
authors.forename: Alberto
authors.initials: A
authors.lastname: Abad
authors.forename: Roberto
authors.initials: R
authors.lastname: Barrio
authors.forename: Angeles
authors.initials: A
authors.lastname: Dena