# JANUS: A bit-wise reversible integrator for N-body dynamics

## TL;DR

JANUS is a novel N-body integrator that achieves exact time-reversal symmetry by combining integer and floating point arithmetic, enabling more accurate long-term simulations of Hamiltonian systems.

## Contribution

The paper introduces JANUS, a new explicit integrator that is symplectic, Liouville-preserving, and exactly time-reversible, improving upon existing numerical schemes.

## Key findings

- JANUS is fast and accurate for long-term Solar System simulations.
- It maintains exact time-reversal symmetry through combined arithmetic.
- JANUS's adjustable order enhances flexibility for various problems.

## Abstract

Hamiltonian systems such as the gravitational N-body problem have time-reversal symmetry. However, all numerical N-body integration schemes, including symplectic ones, respect this property only approximately. In this paper, we present the new N-body integrator JANUS, for which we achieve exact time-reversal symmetry by combining integer and floating point arithmetic. JANUS is explicit, formally symplectic and satisfies Liouville's theorem exactly. Its order is even and can be adjusted between two and ten. We discuss the implementation ofJANUS and present tests of its accuracy and speed by performing and analyzing long-term integrations of the Solar System. We show that JANUS is fast and accurate enough to tackle a broad class of dynamical problems. We also discuss the practical and philosophical implications of running exactly time-reversible simulations.