Note: the starting times (note change!!) are modified as following:

MONDAYs: Lecture start at 8.15 (with a 10 minutes break 9.00-9.10)

TUESDAYs: Lecture start at 10.20 (with a 10 minutes break 10.05-11.15)

Recordings are NOT Recordings are NOT available for this class.   Only the first class is recorded (link above). The lecture notes (available under the Downloads Tab) cover quite systematically the lecture content. A list of topics covered and references to the notes is available here below.

List of Topics covered (with references to Lecture notes Sections):

• Lecture 1 (Monday, 16/2): Introduction and overview (Section 1.1)
• Lecture 2 (Tuesday, 17.2): The logistic family; graphical analysis, attracting and repelling fixed points (Section 1.2, with all subsections)
• Lecture 3 (Monday 23/2) Rotations of the circle: dichotomy for rotations and Weyl equidistribution (Section 1.3)
• Lecture 4 (Tuesday, 24/2) The doubling map: periodic points, shift map and (semi)-conjugacies (beginning of Section 1.5, Sec 1.5.1, Sect. 1.5.2 until Prop.1).
• Lecture 5 (Monday 2/3 The doubling map continued: itineraries and coding (Sec 1.5.2, existence of dense orbits (completed Sec 1.5), definition of baker map (beginning of Sec. 1.7)
• Lecture 6 (Tuesday 3/3) Itineraries and conjugaces for the baker map (completed Sec. 1.7), definition of the CAT map (beginning Sec. 1.8)
• Lecture 7 (Monday 9/3) The CAT map and hyperbolic toral automorphisms: definition of hyperbolicity and results on periodic points (completed Section 1.8)
• Lecture 8 (Tuesday 10/3) Gauss map and continued fractions (Section 1.9), definition of topological dynamical systems and examples of metric spaces (beginning of Sect 2.1)
• Lecture 9 (Monday 16/3) First topological properties: transitivity, minimality, topological mixing (Sec 2.1.1. without example of baker map)
• Lecture 10 (Tuesday 17/3) top. mixing for the baker map (Prop. 2 in Sect 2.1.1), Topological conjugacies (Sec. 2.2.1), properties and examples (Extra: Minkowski question mark function); Definition of SDIC and expansivity (Sec. 2.2.2),
• Lecture 11 (Monday 23/3) examples of expansive (doubling map), and SDIC but not expansive (CAT map) and definition of Devanay chaotic (Sec 2.2.2); introduction to topological entropy (Sec. 2.3); definition of separated sets (beginning of Sec 2.3.1);
• Lecture 12 (Tuesday 24/3) definition of topological entropy via seprated sets (Sec 2.3.1) and equivalence of definition via spanning sets (Sec 2.3.2); computation of entropy of the doubling map and of the rotation;
• Lecture 13 (Monday 30/3): Entropy of the CAT map building separating and spanning sets (Sec. 2.4.1); definition entropy via covers (beginnig of Sec 2.4.2);
• Lecture 14 (Tuesday 31/3): Equivalence of definition of entropy of via covers (Sec 2.4.2); Symbolic coding, shift spaces (Sec 2.5) and definition of a topological Markov chain (Def. 2.5.3 in Sec. 2.5);
• Lecture 15 (Tuesday 14/4): Graph associated to a Markov chain (Sec. 2.5 continued) and number of paths Lemma (Lemma 2.5.2 in Sec. 2.5); Distance, balls and cylinders for a shift space (beginning of Sec 2.6); definition of irreducibility and aperiodicity/primitivity and condition of topological transitivity and topological mixing (end of Sec 2.6)