2020/01/05 by M. Antoñana, Mikel Antoñana, Antoñana, M. +8
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Dynamical Systems (math.DS) #Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Mathematics #FOS: Physical sciences #Numerical methods for differential equations #Pulsars and Gravitational Waves Research #astro-ph.EP #math.DS
paper · pdf · doi:10.48550/arxiv.2001.01221
26 pages; acknowledgments added; remarks 5 and 7 added in second version; remark 4 added and a few minor changes made in third version
openalex publication_date 2020/01/05 · arxiv created 2020/05/21 · arxiv updated 2020/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work considers the \em gravitational N-body problem and introduces global time-renormalization \em functions that allow the efficient numerical integration with fixed time-steps. First, a lower bound of the radius of convergence of the solution to the original equations is derived, which suggests an appropriate time-renormalization. In the new fictitious time τ, it is then proved that any solution exists for all τ∈ ℝ, and that it is uniquely extended as a holomorphic function to a strip of fixed width. As a by-product, a global power series representation of the solutions of the N-body problem is obtained. Noteworthy, our global time-renormalizations remain valid in the limit when one of the masses vanishes. Finally, numerical experiments show the efficiency of the new time-renormalization functions for some N-body problems with close encounters.