Finite-dimensional maps and dendrites with dense sets of end points

Dense Set of Negative Schwarzian Maps Whose Critical Points Have Minimal Limit Sets

We study C2-structural stability of interval maps with negative Schwarzian. It turns out that for a dense set of maps critical points either have trajectories attracted to attracting periodic orbits or are persistently recurrent. It follows that for any structurally stable unimodal map the ω-limit set of the critical point is minimal.

On Finite-dimensional Maps

Let f : X → Y be a perfect surjective map of metrizable spaces. It is shown that if Y is a C-space (resp., dimY ≤ n and dim f ≤ m), then the function space C(X, I ∞ ) (resp., C(X, I 2n+1+m )) equipped with the source limitation topology contains a dense Gδ-set H such that f ×g embeds X into Y × I ∞ (resp., into Y × I 2n+1+m ) for every g ∈ H. Some applications of this result are also given.

Semi-θ-Open Sets and New Classes of Maps

Geometry of Geometrically Finite One-Dimensional Maps

We study the geometry of certain one-dimensional maps as dynamical systems. We prove the property of bounded and bounded nearby geometry of certain C one-dimensional maps with finitely many critical points. This property enables us to give the quasίsymmetric classification of geometrically finite one-dimensional maps.

Gröbner Basis Structure of Finite Sets of Points

We study the relationship between certain Gröbner bases for zerodimensional radical ideals, and the varieties defined by the ideals. Such a variety is a finite set of points in an affine n-dimensional space. We are interested in monomial orders that “eliminate” one variable, say z. Eliminating z corresponds to projecting points in n-space to (n − 1)-space by discarding the z-coordinate. We show...