# Block regularisation of the logarithm central problem

## TL;DR

This paper proves that the logarithm central force problem in two dimensions can be smoothly extended over the singularity at the origin through a process called block regularization, enabling better understanding of its dynamics.

## Contribution

It introduces the concept of block regularization for the logarithm central force problem, showing the flow can be extended over the singularity after re-parametrization.

## Key findings

- Flow can be continuously extended over the singularity
- The problem is block regularizable after re-parametrization
- Provides a new approach to singularity handling in gravitational potentials

## Abstract

The logarithm function is the gravitational potential in $\mathbb{R}^2$. We prove that the logarithm central force problem is block regularizable, that is, the (incomplete) flow may be continuously extended over the singularity at the origin after an appropriate re-parametrization.