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For someone with a Masters degree in pure mathematics?

user242318
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    First off, Fractals and Dynamical Systems are two very different subjects while Chaos might be viewed as a sub-topic of Dynamical Systems. Furthermore, both subjects are quite broad - particularly Dynamical Systems. So I think you'd really need to focus the question quite a lot to get a reasonable response. – Mark McClure Sep 06 '16 at 10:34

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I could recommend Glendinning's Stability, Instability and Chaos.

Will go into quite some detail about dynamical systems and chaos, though not fractals. This book was closely related to a course I took which is why I recommend it, though I have not studied it in detail.

A great Math.SE thread covering book requests for Dynamical Systems, which mentions the above book, is Recommendation for a book and other material on dynamical systems

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ShakesBeer
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