# Hamilton's Dynamics in Complex Phase Space

## TL;DR

This paper extends Hamiltonian dynamics into complex phase space, deriving new equations of motion and illustrating the approach with harmonic motion trajectories in both real and complex spaces.

## Contribution

It introduces a formulation of Hamiltonian dynamics in complex phase space, including the imaginary component in Hamilton's function and deriving the associated equations of motion.

## Key findings

- Complex phase space trajectories differ from real ones.
- Hamilton's equations can be extended to include imaginary parts.
- Harmonic motion examples illustrate the complex dynamics.

## Abstract

We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple harmonic motion are considered and the corresponding trajectory are plotted on real and complex phase space.