# On the Lyapunov instability in Newtonian dynamics

## TL;DR

This paper proves Lyapunov instability in Newtonian systems where the potential energy reaches a local minimum on a hypersurface, extending previous results to include several real analytic cases not covered before.

## Contribution

It introduces a new proof of Lyapunov instability applicable to real analytic potentials at local minima on hypersurfaces, broadening the scope of known instability conditions.

## Key findings

- Lyapunov instability established for specific potential energy configurations
- Extends previous results to real analytic cases
- Applicable to systems with local minima on hypersurfaces

## Abstract

We prove Lyapunov instability for cases in which the local minimum of the potential energy is reached on a hypersurface of the configuration space. In contrast to the known results in this direction, which hold for potentials satisfying hypotheses in the first non-zero jet, this new result covers several real analytic cases that the previous ones do not.