We study a two parameter family of piecewise linear transformations on the interval [0, 1] which have negative slope. We show that the nonwandering set consists of finitely many periodic orbits and an invariant set L which is topologically transitive and the disjoint union of finitely many closed intervals. We determine the number of these intervals.

We construct a one-parameter family of properly embedded minimal annuli in the Heisenberg group Nil3 endowed with a left-invariant Riemannian metric. These annuli are not rotationally invariant. This family gives a vertical half-space theorem and proves that each complete minimal graph in Nil3 is entire. Also, the sister surface of an entire minimal graph in Nil3 is an entire constant mean curv...

We consider an Axiom A diffeomorphism and the invariant set of orbits which never falls into a fixed hole. We study various aspects of the complexity of the symbolic representation of Ω. Our main result are that each topologically transitive component of Ω is coded and that typically Ω is of finite type.

In subsequent papers I propose to investigate various properties of fibre spaces. The object of the fundamental Hurewicz-Steenrod definition is to state a minimum set of readily verifiable conditions under which the covering homotopy theorem holds. An apparent defect of their definition is that it is not topologically invariant. In fact, for topological space X and metrizable non-compact space ...

We show that for a complete complex algebraic variety the pure term of the weight filtration in homology coincides with the image of intersection homology. Therefore pure homology is topologically invariant. To obtain slightly more general results we introduce image homology for noncomplete varieties.

We construct examples of topologically conjugate unimodal maps, such that both of them have an absolutely continuous invariant measure, but for one of them that measure is finite, and for another one it is σ-finite and infinite on every interval. The work is based on the results of Al-Khal, Bruin and Jakobson [2].

Abstract. General topologically invariant microscopical expressions for quantum numbers of particlelike solitons (“skyrmions”) are derived for a class of (2+1)D models. Skyrmions are either half-integer spin fermions with odd electric charge or integer spin bosons with even charge. So they cannot be Anderson’s spinons or holons. General results are exemplified by a square lattice model reminisc...

We consider an Axiom A diffeomorphism and the invariant set of orbits which never falls into a fixed hole. We study various aspects of the complexity of the symbolic representation of Ω. Our main result are that each topologically transitive component of Ω is coded and that typically Ω is of finite type.