The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are much extended
, now including systems that are; (1) non-Hamiltonian, conservative; (2) Hamiltonian with time-dependent perturbation; (3) non-conservative (with dissipation). These systems cover various types of N-body gravitating systems of astrophysical and cosmological interest, such as the orbital evolution of planets, minor planets, artificial satellites due to tidal, non-tidal perturbations and thermal thrust, evolving close binary stellar systems, and the dynamics of accretion disks.
Extensive N-body simulations are among the key means for the study of numerous astrophysical and cosmological phenomena, so various schemes are developed for possibly higher accuracy computations. We demonstrate the principal possibility for revealin
g the evolution of a perturbed Hamiltonian system with an accuracy independent on time. The method is based on the Laplace transform and the derivation and analytical solution of an evolution equation in the phase space for the resolvent and using computer algebra.
This short note is concerned with a recent paper by N{ae}ss [arXiv:1105.5051]. We explain why the statements in the paper are absolutely irrelevant.
In arXiv:1105.1081, Eriksen and Wehus try to criticise the use of Kolmogorovs stochasticity parameter (KSP) for CMB data analysis. Their discussion is based on a serious misunderstanding of the randomness and Arnolds work. Their note includes numerou
s further inaccuracies and groundless statements. However, this short note is concerned with KSP method only.
