Given any positive sequence {cn}n∈N, we construct orientation preserving homeomorphisms f : R → R such that Fix(f) = Per(f) = {0}, 0 is Lyapunov stable and lim sup |i(f ,0)| cm = ∞. We will use our results to discuss and to point out some strong di erences with respect to the computation and behavior of the sequences of the indices of planar homeomorphisms.

We show that the group G∞ of germs at infinity of orientation-preserving homeomorphisms of R admits no action on the line. This gives an example of a left-orderable group of the same cardinality as Homeo+(R) that does not embed in Homeo+(R). As an application of our techniques, we construct a finitely generated group Γ ⊂ G∞ that does not extend to Homeo+(R) and, separately, extend a theorem of ...

We construct an infinite sequence of pseudo-Anosov homeomorphisms without fixed points and leaving invariant a sequence of orientable measured foliations on the same topological surface and the same stratum of the space of Abelian differentials. The existence of such a sequence shows that all pseudo-Anosov homeomorphisms fixing orientable measured foliations cannot be obtained by the Rauzy-Veec...

If φ and ψ are two continuous real-valued functions defined on a compact topological space X and G is a subgroup of the group of all homeomorphisms of X onto itself, the natural pseudo-distance dG(φ,ψ) is defined as the infimum of L(g) = ‖φ−ψ ◦ g‖∞, as g varies in G. In this paper, we make a first step towards extending the study of this concept to the case of Lie groups, by assuming X = G = S....

Let M be a metric space and let 4>(M) = M be a homeomorphism. 0(m) = X^d^w) is called the orW of m^M under «2> • ■ • (»i<m2...

We introduce and characterize extremal 2-cuts for good fractal necklaces. Using this characterization the related topological properties of 2-cuts, we prove that every necklace has a unique IFS in certain sense. Also, two necklaces admit only rigid homeomorphisms thus group self-homeomorphisms is countable. In addition, weaker co-Hopfian property also obtained.