The aim of this mini course is to introduce basic concepts of discrete one-dimensional dynamical systems through the unimodal family of interval maps. We primarily focus on topological, symbolic and combinatorial aspects of the theory.

1. Bifurcation diagram of the logistic family, Feigenbaum universality and chaos
(asymptotic behavior of orbits of logistic maps, hyperbolicity and bifurcations, renormalization, Feigenbaum constants and chaos)

2. Symbolic dynamics and kneading theory for unimodal maps
(Milnor-Thurston kneading theory, full families, formation of periodic orbits and topological entropy)

3. Piecewise-linear model and attractors
(construction of semi-conjugacy to tent maps, Markov partitions and substitutions, nonwandering and omega-limit sets, attractors of unimodal maps)

Ana Anusic, Faculty of Electrical Engineering and Computing, University of Zagreb.