Valuations and hyperbolicity in dynamics

Ward T.

Table of contents :
1. Introduction……Page 2
2.1. Definition and examples……Page 3
2.2. Background on adeles……Page 7
2.3. Adelic covering space……Page 8
2.4. Topological entropy……Page 10
2.5. Dynamical properties……Page 12
2.6. Periodic points……Page 13
2.7. Growth rates……Page 15
2.8. Typical group automorphisms……Page 19
3. Bernoullicity and recurrence……Page 24
3.1. Automorphisms of solenoids……Page 25
3.3. Commuting automorphisms……Page 27
4. Mixing……Page 28
4.1. Background from algebra……Page 30
4.2. Order of mixing — connected case……Page 32
4.3. Order of mixing — disconnected case……Page 33
5. Subdynamics……Page 40
5.1. Examples……Page 44
5.2. Adelic amoebas……Page 47
6.2. Periodic points……Page 49
6.5. Entropy and Deligne periods……Page 50
References……Page 51