کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6425982 1345399 2012 41 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Ergodic properties of boundary actions and the Nielsen-Schreier theory
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Ergodic properties of boundary actions and the Nielsen-Schreier theory
چکیده انگلیسی

We study the basic ergodic properties (ergodicity and conservativity) of the action of an arbitrary subgroup H of a free group F on the boundary ∂F with respect to the uniform measure. Our approach is geometrical and combinatorial, and it is based on choosing a system of Nielsen-Schreier generators in H associated with a geodesic spanning tree in the Schreier graph X=H∖F. We give several (mod 0) equivalent descriptions of the Hopf decomposition of the boundary into the conservative and the dissipative parts. Further, we relate conservativity and dissipativity of the action with the growth of the Schreier graph X and of the subgroup H (≡ cogrowth of X), respectively. We also construct numerous examples illustrating connections between various relevant notions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 230, Issue 3, 20 June 2012, Pages 1340-1380
نویسندگان
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