Dynamical systems course notes.
I have added some exercise sheets (would be happy to hear about errors in lectures/exercise sheets).

  M2 AAG/MdA: Dynamical systems 2019

Lecture 1: Chap 01 (2019):   Lecture   Exercises     Introduction to Dyn Sys.
Lecture 2: Chap 02 (2019):   Lecture   Exercises     Dyn Sys and invariant measures.
Lecture 3: Chap 03 (2019):   Lecture   (no exos)     The Hilbert metric and Birkhoff's inequality.
Lecture 4.1: Chap 04 (2019):   Lecture   Exercises     Cone contractions and spectral gap.
Lecture 4.2: Chap 05 (2019):   Lecture   (exos from chap 04)     A family of Log-Lipschitz cones.
Lecture 5: Chap 06 (2019):   Lecture   (exos from chap 04)     Positive transfer operators and spectral gap.
Lecture 6: Chap 07 (2019):   Lecture   Exercises   Solution-sketch     The pressure function and CLT.
Lecture 7: Chap 08 (2019):   Lecture   Exercises     Dimension theory and Gibbs measure.
Lecture 8: Chap 09 (2019):   Lecture   Exercises     Complex dynamics and dimensions.
Lecture 9: Chap 10 (2019):   Lecture   (no exos)     Hyperbolic dynamics. s/u-manifolds.
Lecture 10: Chap 11 (2019):   Lecture   Exercises     The Poincare disk and geodesic flows.

Chap 1: Basics of Ergodic theory
Chap 2: Birkhoff and v Neumann ergodic thms
Chap 3 (2018): Factors and Isomorphisms
Chap 4 (2017): Invariant Measures
Chap 5 (2017): Gauss map and Continued Fractions
Chap 6 (2017): Hilbert metric and cones
Chap 7 (2017): Spectral Gap theorems
   (2018 added page 5:) Log-Lipschitz family
   (2017): Cones and Gibbs measures
   (2017 added:) Large Deviation example
Chap 8 (2017): Metric entropy (of a measure)
Chap 9 (2018): Gibbs measure + CLT

Perhaps to include: Kingmans's subergodic Thm

  Part II : Dynamical systems (old stuff)  

Chap 1: Topological dynamics
(not done in details) Symbolic dynamics
Chap 2: Topological Entropy
Chap 3 (2016): Hausdoff dimension and Bowen's formula
   Added 2017: (new complex dynamics part)
   Added 2017: (new local-dim-Bowen part)
Chap 4: Arnold - Small Divisors
   2017: (newer version of Arnold's Thm)
   2018: (version in French) Diffeo du cercle - Thm d'Arnold
Chap 5: Hyperbolic Dynamics
   Added 2017: (Unstable manifold theorem)
   Added 2017: (Uniformly Hyperbolic/Anosov)

Perhaps to include: Geodesic flow