Dynamical Systems of Algebraic Origin
Although the study of dynamical systems is mainly concerned with single trans formations and one-parameter flows (i. e. with actions of Z, N, JR, or JR+), er godic theory inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multi-...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser
1995, 1995
|
| Edition: | 1st ed. 1995 |
| Series: | Progress in Mathematics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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