Vershik, A. M. Dynamic theory of growth in groups: Entropy, boundaries, examples. (English. Russian original) Zbl 0991.37005 Russ. Math. Surv. 55, No. 4, 667-733 (2000); translation from Usp. Mat. Nauk 55, No. 4, 59-128 (2000). This is an expository paper of the following topics: (1) Numerical invariants of countable free groups. (2) An ergodic method for constructing the boundaries of random walks, the entropy of the boundary polymorphism. (3) A geometric realization of the free solvable groups and their boundaries. (4) Dynamical structure of local and locally free groups. (5) Secondary entropy of \(K\)-automorphisms. Reviewer: Yasuhiro Asoo (Okayama) Cited in 5 ReviewsCited in 48 Documents MSC: 37A35 Entropy and other invariants, isomorphism, classification in ergodic theory 28D20 Entropy and other invariants Keywords:entropy; growth of free groups; boundary PDFBibTeX XMLCite \textit{A. M. Vershik}, Russ. Math. Surv. 55, No. 4, 667--733 (2000; Zbl 0991.37005); translation from Usp. Mat. Nauk 55, No. 4, 59--128 (2000) Full Text: DOI