Phase Space

Phase space is given by the vector $(x,\dot{x})\in {\mathbb{R}}^{2n}$, where:

• $x\in {\mathbb{R}}^n$ is the Particle’s position.
• $\dot{x}:=\frac{d}{dt}x\in {\mathbb{R}}^n$ is the Particle’s velocity.

Phase space allow us to describe the movement of a set of Particle’s without requiring knowledge of it’s past and future, i.e. it simplifies problems by following Markovian Dynamics.

Interactive tutorial

Intro to Phase Space singularity analysis, using a Google Colab notebook