We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

We prove results showing that the existence of essential maps of surfaces in a manifold M̄ obtained from a 3-manifold M by Dehn filling implies the existence of essential maps of surfaces in M .

Using the Birman exact sequence for pure mapping class groups, we construct a universal Cannon-Thurston map onto boundary of curve complex surface with punctures call surviving complex. Along way prove hyperbolicity this and identify its as space laminations. As corollary obtain to ordinary complex, extending earlier work second author Mj Schleimer [Comment. Math. Helv. 86 (201...

The sequences of azurin and titin, sandwich proteins, are analyzed based on inter-residue average distance statistics. A kind of predicted contact map based on inter-residue average distance statistics (Average Distance Map, ADM) is used to pinpoint regions of possible compact regions for two proteins. We compare predicted compact regions with the positions of the residues with experimental hig...

A well known result on pseudodifferential operators states that the noncommutative residue (Wodzicki residue) of a pseudodifferential projection vanishes. This statement is non-local and implies the regularity of the eta invariant at zero of Dirac type operators. We prove that in a filtered algebra the value of a projection under any residual trace depends only on the principal part of the proj...

This paper further develops the theory of arbitrary semigroups acting on trees via elliptic mappings. A key tool is the Lyndon-Chiswell length function L for the semigroup S which allows one to construct a tree T and an action of S on T via elliptic maps. Improving on previous results, the length function of the action will also be L.