Arnaud Hilion

R-trees, dual laminations and compact systems of partial isometries

Let FN be a free group of finite rank N 2, and let T be an R-tree with a very small, minimal action of FN with dense orbits. For any basis A of FN there exists a heart KA ⊂ T (= the metric completion of T) which is a compact subtree that has the property that the dynamical system of partial isometries ai : KA ai KA → a −1 i KA KA, for each ai ∈ A, defines a tree T(KA,A) which contains an isometric copy of T as minimal subtree.

Ergodic currents dual to a real tree

Let

Growth and order of automorphisms of free groups and free Burnside groups

T

Free group automorphisms with parabolic boundary orbits

be an

Non-unique ergodicity, observers' topology and the dual algebraic lamination for

\R

\Bbb R

-tree in the boundary of Outer space with dense orbits. When the free group

-trees

\FN

Rips induction: index of the dual lamination of an

acts freely on

\mathbb{R}

T

-tree

, we prove that the number of projective classes of ergodic currents dual to