Are numerical studies of long term dynamics conclusive: the case of the Hénon map

International Workshop on Nonlinear Maps and Applications 2015

Galias, Zbigniew^1

AGH University of Science and Technology, Department of Electrical Engineering, al. Mickiewicza 30, Kraków

30-059, Poland^1

关键词: Double precision;    Long term dynamics;    Number of iterations;    Periodic windows;    Random initial conditions;    Steady-state behaviors;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/692/1/012001/pdf
DOI  :  10.1088/1742-6596/692/1/012001

来源: IOP

【 摘 要 】

Numerical studies of the Hénon map show that there is an abundance of periodic windows close to classical parameter values. In this work properties of these periodic windows are studied. It is shown that in order to detect periodic windows in simulations one has to compute trajectories in a sufficient precision, which in many cases is much higher than the standard double precision. Moreover, it is shown that even if computations are carried out in a sufficient precision, one may need an extremely large number of iterations to observe convergence to a sink starting from random initial conditions, and hence the underlying steady state behavior may be practically undetectable using the standard trajectory monitoring based approach.