A set of positive Gaussian measure with uniformly zero density everywhere.

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

A Constructible Set of Normals with Positive Measure

A C1 Map with Invariant Cantor Set of Positive Measure

Many examples exist of one-dimensional systems that are topologically conjugate to the shift operator on Σ2 and are thus chaotic. Most of these examples which have invariant Cantor subsets, have Cantor subsets of measure zero. In this paper we outline the formulation of a C map on a closed interval that has an invariant Cantor subset of positive Lebesgue measure. We also survey techniques used ...

The Limit Set of the Handlebody Set Has Measure Zero

This note fixes a small gap in the proof in [4] that the limit set of the handlebody set has measure zero.

Density near zero

Let $S$ be a dense subsemigroup of $(0,+infty)$. In this paper, we state   definition of thick near zero, and also  we will introduce a definition that is equivalent to the definition of piecewise syndetic near zero which presented by Hindman  and Leader in [6].  We define density near zero for subsets of $S$ by a collection of nonempty finite subsets of $S$ and we investigate the conditions un...