Document Zbl 0991.37005

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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 Reviews

Cited in 54 Documents

MSC:

37A35	Entropy and other invariants, isomorphism, classification in ergodic theory
28D20	Entropy and other invariants

Keywords:

entropy; growth of free groups; boundary

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