Hi, I am working towards a PhD in Mechanical engineering and my area of focus is Energy Harvesting/ Vibration control. We do a lot of formulation of electromechanical systems and analyze them using tools from Perturbation theory and control systems. Doing all this, I have developed an interest in understanding the foundations of nonlinear dynamics and chaos. To dig deep into it, I started finding sources for understanding Dynamical systems theory in detail. However, since I don't have a mathematics background, I have to understand everything from basics. There are two approaches which I can make out to learn on my own.
One is bottom up, where I start learning basics of Topology, Abstract Algebra, Differential equations and then pick up resources on Dynamical systems theory. Another is top down where I start learning Dynamical systems theory and learn other things along the way. What does r/math suggest I should do? Also a side question: should I ask my advisor for a project which is more related to chaos in the later years of my PhD. I got interested in the field after taking graduate course (in mechanical engineering) in nonlinear vibrations and chaos theory.
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from math https://ift.tt/2MCj727
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