Analyticity of iterates of random non-expansive maps

Random Iterates of Monotone Maps

Dynamics of non-expansive maps on strictly convex Banach spaces

This paper concerns the dynamics of non-expansive maps on strictly convex finite dimensional normed spaces. By using results of Edelstein and Lyubich, we show that if X = (R, ‖ · ‖) is strictly convex and X has no 1-complemented Euclidean plane, then every bounded orbit of a non-expansive map f : X → X , converges to a periodic orbit. By putting extra assumptions on the derivatives of the norm,...

Expansive Maps of the Circle

After preparing this note, the paper [IT] was discovered which covers the more general situation of “expansive foliations”, and in codimension one their result includes Theorem1.2. We note that the proof given here is more self–contained and goes into more detail about the construction of the “ping-pong table” in the topological case, which the reader might still find of interest. Ralf Spatzier...

Equicontinuity of Iterates of Circle Maps Antonios

Let f be a continuous map of the circle to itsel Necessary and sufficient conditions are given for the family ofiterates {f"}= to be equicontinuous.

Lattice Isomorphisms and Iterates of Nonexpansive Maps

It is easy to see that the I, norm and the sup norm 11. Ilm (Ilxll, = max{Ix, I: 1 I i 5 n)) on I?’ are polyhedral. If E is a finite dimensional Banach space with a polyhedral norm 11. )I, D is a compact subset of E and f: D + D is a nonexpansive map, Weller [2] has shown that for each x E D, there again exists an integer px such that (1.1) holds. The original arguments did not give upper bound...