Duality with expanding maps and shrinking maps, and its applications to Gauss maps

Nonuniformly Expanding 1D Maps

This paper attempts to make accessible a body of ideas surrounding the following result: Typical families of (possibly multi-model) 1-dimensional maps passing through “Misiurewicz points” have invariant densities for positive measure sets of parameters. The simplest paradigms of chaotic behavior in dynamical systems are found in uniformly expanding and uniformly hyperbolic (or Anosov) maps. All...

Relative Compactness and Product Stable Quotient Maps

Using Gauss Maps to Detect Intersections

A family of compact submanifolds with boundary has a nonempty stable interior intersection in R provided a certain geometric estimate holds. As a global application we establish a sharp intersection criterion for a family of properly embedded mj -dimensional submanifolds Mj ⊂ R that is based solely on their Gauss maps Gj : Mj → G(n−mj , n) , Gj(p) = [TpMj ]⊥ .

Foliations with Degenerate Gauss Maps on P

We obtain a classification of codimension one holomorphic foliations on P with degenerate Gauss maps.

Evolution maps and applications

Common tasks in document analysis, such as binarization, line extraction etc., are still considered difficult for highly degraded text documents. Having reliable fundamental information regarding the characters of the document, such as the distribution of character dimensions and stroke width, can significantly improve the performance of these tasks. We introduce a novel perspective of the imag...