Dynamical Systems of Algebraic Origin

I. Group actions by automorphisms of compact groups.- 1. Ergodicity and mixing.- 2. Expansiveness and Lie subshifts.- 3. The descending chain condition.- 4. Groups of Markov type.- II. ?d-actions on compact abelian groups.- 5. The dual module.- 6. The dynamical system defined by a Noetherian module.- 7. The dynamical system defined by a point.- 8. The dynamical system defined by a prime ideal.- III. Expansive automorphisms of compact groups.- 9. Expansive automorphisms of compact connected groups.- 10. The structure of expansive automorphisms.- IV. Periodic points.- 11. Periodic points of ?d-actions.- 12. Periodic points of ergodic group automorphisms.- V. Entropy.- 13. Entropy of ?d-actions.- 14. Yuzvinskii's addition formula.- 15. ?d-actions on groups with zero-dimensional centres.- 16. Mahler measure.- 17. Mahler measure and entropy of group automorphisms.- 18. Mahler measure and entropy of ?d-actions.- VI. Positive entropy.- 19. Positive entropy.- 20. Completely positive entropy.- 21. Entropy and periodic points.- 22. The distribution of periodic points.- 23. Bernoullicity.- VII. Zero entropy.- 24. Entropy and dimension.- 25. Shift-invariant subgroups of $$ {(\mathbb{Z}/p\mathbb{Z})^{{{\mathbb{Z}^2}}}} $$.- 26. Relative entropies and residual sigma-algebras.- VIII. Mixing.- 27. Multiple mixing and additive relations in fields.- 28. Masser's theorem and non-mixing sets.- IX. Rigidity.- 29. Almost minimal ?d-actions and invariant measures.- 30. Cohomological rigidity.- 31. Isomorphism rigidity.