Bulletin of the Brazilian Mathematical Society, New Series

Conze, J.; Hervé, L.; Raugi, A.

doi: 10.1007/BF01235987pmid: N/A

We applied results from [2] to multiresolution analysis and to lattice tilings of ℝ d with self-affine tiles.

Contreras, Gonzalo; Ruggiero, Rafael

doi: 10.1007/BF01235988pmid: N/A

We construct examples ofC 3 compact surfaces of non-positive curvature having non-Anosov geodesic flows and satisfying the following property: there existsL>0 such that the area of every ideal triangle in the universal covering of the surface is bounded above byL.

Ruggiero, Rafael

doi: 10.1007/BF01235989pmid: N/A

Let M be aC k ,k ≥ 4, compact surface of genus greater than two whose curvature is negative in all points but along a simple closed geodesic γ(t) where the curvature is zero at every point. We show that the area of ideal triangles having a lifting of γ as an edge is infinite. This provides a family of surfaces having ideal triangles of infinite area whose geodesic flows are equivalent to Anosov flows, in contrast with the well-known examples of surfaces with flat strips which also have ideal triangles of infinite area. By the CAT-comparison theory we can deduce, using these surfaces as models, that aC ∞ compact surface of non-positive curvature having one geodesic along which the curvature is zero has ideal triangles of infinite area.

Matsumoto, Shigenori

doi: 10.1007/BF01235990pmid: N/A

We consider the rotation setR of a homeomorphismf, isotopic to the identity, of a closed surface Σ of genusg≤2. We show if Int(R) is nonempty and contains an element which is realized by an asymptotic measure, then all the rational points of Int(R) are realized by periodic orbits. We raise an example to show that the second condition above is indispensable ifg≥2. We also show that ifR contains a (g+1)-simplex whose vertices are realizable by periodic orbits, then the topological entropy off is positive.

Ivanov, A.; Tuzhilin, A.

doi: 10.1007/BF01235991pmid: N/A

The aim of this paper is to get an effective restriction on the topologies of minimal 2-trees in terms of twisting numbers of the trees and the convexity levels number of the trees boundaries.