The entropy of solvable groups

Ergodic Theory and Dynamical Systems

Volumn 23, Issue 3, 2003, Pages 907-918

  Osin, D V ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037874962     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385702000937     Document Type: Article

References (33)

1. A. Aves. Entropie des groupes de type fini. C. R. Acad. Sc. Paris, Sér. A 275 (1972), 1363-1366.
2. H. Bass. The degree of polynomial growth of finitely generated nilpotent groups. Proc. London Math. Soc. 25 (1972), 603-614.
3. M. Bucher and P. de la Harpe. Free products with amalgamation and HNN-extensions which are of uniformly exponential growth. Math. Notes 67(6) (2000), 811-815.
4. V. A. Efremovich. The proximity geometry of Riemannian manifolds. Uspekhi Mat. Nauk. 8 (1953), 189 (in Russian).
5. E. Følner. On groups with full Banach mean value. Math. Scand. 3 (1955), 243-254.
6. R. I. Grigorchuk. Degrees of growth of finitely generated groups and the theory of invariant means. Math. USSR Izv. 25(2) (1985) 259-300.
7. R. I. Grigorchuk. On growth in group theory. Proc. Int. Cong. of Mathematicians, Kyoto, 1990, Vol. I. The Mathematical Society of Japan, 1991, pp. 325-338.
8. R. I. Grigorchuk and M. J. Mamaghani. On use of iterates of endomorphisms for constructing groups with specific properties. Preprint, University of Teheran, 1996.
9. R. I. Grigorchuk and P. de la Harpe. On problems related to growth, entropy, and spectrum in group theory. J. Dynam. & Control Sys. 3 (1997), 51-89.
10. R. I. Grigorchuk and P. de la Harpe. Limit behavior of exponential growth rates for finitely generated groups. Preprint, University of Geneva, 1999.
11. R. I. Grigorchuk and P. de la Harpe. One-relator groups of exponential growth have uniformly exponential growth. Math. Notes 69 (2001), 628-630.
12. M. Gromov. Groups of polynomial growth and expanding maps. Inst. Hautes Etudes Sci. Publ. Math. 53 (1981), 53-73.
13. M. Gromov, J. Lafontaine and P. Pansu. Structures métriques pour les variétés riemanniennes. Fernand Nathan, Paris, 1981.
14. Y. Guivarc'h. Croissance polynomial et périodes des functions harmoniques. Bull. Soc. Math. France 101 (1973), 333-379.
15. Ph. Hall. Nilpotent groups. Canad. Math. Congr. Univ. Alberta. Queen Mary College, 1954.
16. P. de la Harpe. Topics in Geometric Group Theory. University of Chicago Press, 2000.
17. H. Hasse. Number Theory. Springer, Berlin, 1980.
18. A. Karrass, W. Magnus and D. Solitar. Combinatorial group theory. Presentations of Groups in Terms of Generators and Relations. Dover, New York, 1976.
19. M. I. Kargapolov and Ju. I. Merzljakov. Fundamentals of the Theory of Groups. Springer, Berlin, 1979.
20. M. Koubi. Croissance uniforme dans les groupes hyperboliques. Ann. Inst. Fourier 48 (1998), 1441-1453.
21. S. Lang. Algebra. Addison-Wesley, Reading, MA, 1965.
22. A. Manning. Topological entropy for geodesic flows. Ann. Math. 110 (1979), 567-573.
23. J. Milnor. A note on the fundamental group. J. Differential Geom. 2 (1968), 1-7.
24. J. Milnor. Problem 5603. Amer. Math. Monthly 75(6) (1968), 685-686.
25. J. Milnor. Growth of finitely generated solvable groups. J. Differential Geom. 2 (1968), 447-449.
26. D. Segal. Polycyclic Groups. Cambridge University Press, Cambridge, 1983.
27. A. S. Švarc. Volume invariants of coverings. Dokl. Akad. Nauk. 105 (1955), 32-34 (in Russian).
28. P. B. Shalen and P. Wagreich. Growth rates, Zp homology, and volumes of hyperbolic 3-manifolds. Trans. Amer. Math. Soc. 331 (1992), 895-917.
29. J. Tits. Free subgroup in linear groups. J. Algebra 20 (1979), 250-270.
30. J. Tits. Appendix to 'Groups of polynomial growth and expanding maps' by M. Gromov. Inst. Hautes Etudes Sci. Publ. Math. 53 (1981), 74-78.
31. J. Tits. Groupes à croissance polynomial. Séminaire Bourbaki. Vol. 1980/81 (Lecture Notes in Mathematics, 901). Springer, Berlin, 1981, pp. 176-178.
32. P. Walters. An Introduction to Ergodic Theory (Graduate Texts in Mathematics, 79). Springer, Berlin, 1982.
33. J. A. Wolf. Growth of finitely generated solvable groups and curvature of Riemannian manifolds. J. Differential Geom. 2 (1968), 421-446.