Not really my field of study, just on a hobbyist level I got into nonlinear dynamics. All started with Steven Strogatz' book sync. https://www.stevenstrogatz.com/books/sync-the-emerging-scien... I then found the amazing intro course on Complexityexplorer: https://www.complexityexplorer.org/courses/136-nonlinear-dyn... by Liz Bradley. Since then I am hooked :)
Why specifically nonlinear dynamics rather than starting with just dynamical systems? Curious because, in my expereince when studying control theory, nonlinear controls is usually one of the courses that is taken later in the sequence after a lot of linear control techniques.
The type of problems in that space usually didn't work well with linear control theory, although I'm not strong in theory ... at the time mostly playing with some signal processing packages in matlab (e.g. Kalman Filtering).
Recently, I got interested in group and social dynamics (we recorded a couple of large scale datasets). I found an approach found in some of the non-linear dynamics practitioner's lectures/works intuitive and fun for me. You could call it "Explorative Experimental Computational Mathematics": 1. find an interesting phenomenon 2. record data, run simulations and plot data 3. look at the visualizations 4. fit a model /formulas based on the visualizations Iterate.
If I have completely misrepresented a field/research please forgive me. Just an enthusiast amateur here.