I now have a full @YouTube playlist of video lectures with coding demonstrations that accompanies every chapter of my book! Check it out here:

Sharkovskii's Theorem has got to be one of the coolest results in all of chaos theory and dynamical systems. I'll tell you all about it here:

A central question in topology is "how much can I bend something without breaking it?" In dynamical systems, this translates to a question of structural stability, which I introduce here:

You've probably been asking yourself "what actually is chaos" throughout my lectures so far. Here I will give the precise definition (according to Devaney):

I'm excited to announce a new paper on ArXiv! Here we show how to adapt data-driven methods for dynamical systems analysis for the low-data limit. We provide the theory and a bunch of interest examples, ranging from fluids to real-world El Nino datasets

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Here I will fully classify chaotic dynamics on a fractal invariant set in terms of infinite binary sequences - a beautiful way of making the complex interpretable:

Abstraction is the language of mathematics. Here I will introduce symbolic dynamics which are a seemingly very abstract concept that turns out to describe many fractal invariant sets in chaotic systems:

Fractals and chaos theory are intertwined in the popular imagination. Here I will show you how fractals arise in even the simplest nonlinear models:

For lecture 2 I will teach you all about hyperbolicity and how it is critical for analyzing discrete-time dynamical systems:

Here's the first lecture for my chaos theory series! I'll teach you all the basics about discrete-time dynamical systems to get us started:

I'm back with another lecture series! This time I'm going to teach you all you need to know about chaos theory. Here's the welcome lecture:

My all-time favourite application of machine learning to dynamical systems is autoencoders. Let me introduce you to them with this video:

I now have a published paper for every year I've been alive! Here's my latest paper accepted to the numerical analysis and modelling journal ESAIM: M2AN:

@YouTube And here's the full code repo to reproduce the results yourself:

Here's a video explaining the contents of my book and what you can expect from my channel going forward:

I've done it! I've finished the complete series of video lectures to complement my book. Here's the last one on model identification with autoencoders:

NEW PREPRINT: Here we use graphon theory to learn transition probabilities of stochastic signals to find coherent sets https://t.co/Zq2SAgZ92w

My penultimate video in this series is now available! Here we learn about how neural networks can learn action-angle coordinates for integrable systems:

Autoencoder neural networks to learn Koopman eigenfunctions? Here's a great one:

In this lecture I use autoencoder neural network architectures to learn normal forms for bifurcations: