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.