A collection of interesting things

Below is a collection of links to this website that are of more general, mostly educational, interest.

Simulate the dynamics of the standard map in your browser

The standard map is one of the paradigmatic systems of Hamiltonian chaotic dynamics. In the linked webpage you can simulate the dynamics of the standard map, and by changing the map's parameter K observe the transition from integrability to chaos.

Compute normal forms

Normal forms provide approximations to the dynamics that capture the dynamical properties in which we are interested. In certain cases, such approximations are even integrable. Several years ago I wrote a journal entry explaining how to compute the normal form of a Hamiltonian system using Mathematica and later I wrote some explanatory notes on how to practically use the code.

Notes on the Kuramoto model and synchronization

I have used the linked slides in the MSc course Complexity and Networks. The notes discuss the sycnhronization in the Kuramoto model, the Ott-Antonsen ansatz, the Master Stability Function, and circle maps in the context of circadian rhytms.

A short introduction to the global geometry of physical systems

One of the main themes of my research is the global geometry of integrable Hamiltonian systems. The linked article is an introduction to the topic for students of Mathematics and Physics.