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I'm looking for a solid, gentle introduction for an undergraduate student with only a calculus background to one-dimensional dynamical systems with an emphasis on chaotic systems. Something that introduces objects like Markov partitions from a combinatorial point of view but avoids discussion of ergodic theory. I would like to work up to something like Sharkovsky's theorem (e.g. the presentation in the Burns and Hasselblatt proof). The references I have been able to find both move a bit too quickly and are surrounded by/develop more difficult concepts simultaneously.

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  • $\begingroup$ Have you seen this book? I am not very sure how gentle is it, but as far as I remember it's a pretty solid reference to 1d dynamics. $\endgroup$ – Evgeny Jun 29 '17 at 16:10
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Devaney's book: An Introduction to Chaotic Dynamical Systems sounds very well-suited to what you're looking for.

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