Attractor of Cantor Type with Positive Measure

We construct an iterated function system consisting of strictly increasing contractions $f,g\colon [0,1]\to [0,1]$ with $f([0,1])\cap g([0,1])=\emptyset$ and such that its attractor has positive Lebesgue measure

Generalized Dimension Distortion under Mappings of Sub-Exponentially Integrable Distortion

We prove a dimension distortion estimate for mappings of sub-exponentially integrable distortion in Euclidean spaces, which is essentially sharp in the plane

Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings

We investigate how the integrability of the derivatives of Orlicz-Sobolev mappings defined on open subsets of $\mathbb{R}^n$ affect the sizes of the images of sets of Hausdorff dimension less than $n$. We measure the sizes of the image sets in terms of generalized Hausdorff measures

A realistic heat bath: theory and application to kink-antikink dynamics

We propose a new method of studying a real-time canonical evolution of field-theoretic systems with boundary coupling to a realistic heat bath. In the free-field case the method is equivalent to an infinite extension of the system beyond the boundary, while in the interacting case the extension of the system is done in linear approximation. We use this technique to study kink-antikink dynamics in $\varphi^4$ field theory in 1+1 dimensions.Comment: 21 pages including 7 figures (the shar file includes the tex file + 7 postscript files for figures). IUHET-241, IPS-92-29, UALG-PHYS-1