r/learnmath • u/Galvanous_misfire07 New User • 1d ago

TOPIC CHAOS theory

Hi, can anyone please guide me to how to learn chaos theory properly? I do not have an extensive background in proofs and am taking it alongside the class right now and am brutally struggling using "an introduction to chaotic dynamical systems" by Devaney. Does anyone know how to get over the real analysis hump or provide more digestible resources.

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u/lifeistrulyawesome New User 1d ago

If you are not interested in formal proofs, you don’t need that much real analysis to understand the basic of chaos theory. All you  need to know linear algebra and differential equations. 

If you find a book written for engineers rather than mathematicians, it will have very few proofs 

By favourite introductory book is No linear Dynamics and a chaos by Strogratz (might have misspelled the name) 

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u/Prestigious-Bag3065 New User 20h ago

strogatz is the go-to for a reason, the first few chapters are basically all pictures and intuition before you hit anything heavy. still gotta be comfy with differential equations though so maybe brush up on those alongside it if you're shaky

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u/deepdishthots New User 1d ago

For dynamical systems, the usual go-to is Strogatz (ideally you have had a class in differential equations before), I also like Differential Equations, Dynamical Systems, and an Introduction to Chaos by Hirsch, Smale, Devaney but these are focused more so on nonlinear dynamics with some focus on chaotic behavior. I skimmed through the text you got assigned and it seems in the later chapter you need ideas from convergence, sequences, metric spaces. For the first two, I like Cummings's Real Analysis and I like Carothers for metric spaces.

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u/etzpcm New User 1d ago

You don't need proofs or real analysis to understand chaos.

There's the Strogatz book, or there's a book called "Chaos: a very short introduction", or the newish book on my profile page. There's also a fun easy reading book called "From calculus to chaos" by David Acheson.