Free group automorphisms with parabolic boundary orbits

Dynamics of free group automorphisms

We present a coarse convexity result for the dynamics of free group automorphisms: Given an automorphism φ of a finitely generated free group F , we show that for all x ∈ F and 0 ≤ i ≤ N , the length of φ(x) is bounded above by a constant multiple of the sum of the lengths of x and φ (x), with the constant depending only on φ.

A Parabolic Free Boundary Problem with Bernoulli Type Condition on the Free Boundary

Consider the parabolic free boundary problem ∆u− ∂tu = 0 in {u > 0} , |∇u| = 1 on ∂{u > 0} . For a realistic class of solutions, containing for example all limits of the singular perturbation problem ∆uε − ∂tuε = βε(uε) as ε → 0, we prove that one-sided flatness of the free boundary implies regularity. In particular, we show that the topological free boundary ∂{u > 0} can be decomposed into an ...

Variational Modeling of Parabolic Free Boundary Problems

Free Boundary Problems for Parabolic Equations

An address delivered at the Ann Arbor meeting of the American Mathematical Society on November 29, 1969, by invitation of the Committee to Select Hour Speakers for Western Sectional Meetings; received by the editors April 9,1969. AMS 1969 subject classifications. Primary 3562, 3578.

Free group automorphisms with many fixed points at infinity

A concrete family of automorphisms αn of the free group Fn is exhibited, for any n ≥ 3, and the following properties are proved: αn is irreducible with irreducible powers, has trivial fixed subgroup, and has 2n− 1 attractive as well as 2n repelling fixed points at ∂Fn . As a consequence of a recent result of V Guirardel there can not be more fixed points on ∂Fn , so that this family provides th...