Dynamical properties of expansive one-sided cellular automata

To every one-sided one-dimensional cellular automatonF with neighbourhood radiusr we associate its canonical factor defined by considering only the firstr coordinates of all the images of points under the powers ofF. Whenever the cellular automaton is surjective, this factor is a subshift which plays a primary role in its dynamics. In this article we study the class of positively expansive one-sided cellular automata, i.e. those that are conjugate to their canonical factors. This class is a natural generalisation of the toggle or permutative cellular automata introduced in [He]. We prove that the canonical factors of positively expansive one-sided cellular automata are mixing subshifts of finite type that are shift equivalent to full shifts. Moreover, the uniform Bernoulli measure is the unique measure of maximal entropy forF. Consequently, their natural extensions are Bernoulli. We also describe a family of non-permutative positively expansive cellular automata. This research was partially supported by action E9314 of ECOS-CONICYT.     

On the Stability Behaviour of Boltzmann's Equation

The Boltzmann equation for an “isolated” gas system is assumed to form a “dynamical system” in a compact subset of the space of continuous distribution functions (existence assumption). Then the asymptotic stability in the sense of Lyapunov of the total Maxwell distribution is investigated (“approach to equilibrium”). Further the influence of persistent perturbations on the stability behaviour of Boltzmann's equation is considered (“structural stability”).     

Über die räumliche Verteilung der Punkte in Gittern mit indefiniter Metrik

Ohne Zusammenfassung     

Necessary and Sufficient Conditions to be an Eigenvalue for Linearly Recurrent Dynamical Cantor Systems

Necessary and sufficient conditions are given for linearly recurrentCantor dynamical systems to have measurable and continuous eigenfunctions.Also an example of a linearly recurrent system with a nontrivialKronecker factor and a trivial maximal equicontinuous factoris constructed explicitly.     

Zur Theorie der Kugelfunktionen einer Matrixvariablen

Ohne Zusammenfassung     

Adaptive wavelet methods and sparsity reconstruction for inverse heat conduction problems

This paper is concerned with the numerical treatment of inverse heat conduction problems. In particular, we combine recent results on the regularization of ill-posed problems by iterated soft shrinkage with adaptive wavelet algorithms for the forward problem. The analysis is applied to an inverse parabolic problem that stems from the industrial process of melting iron ore in a steel furnace. Some numerical experiments that confirm the applicability of our approach are presented.     

Structure of bounded topological-sequence-entropy minimal systems

In this article we prove that a minimal topological dynamicalsystem (X, T) with bounded topological sequence entropy hasthe following structure. Here is the maximal equicontinuous factor of (X, T), ^' and^' are proximal extensions and ^' is a finite-to-one equicontinuousextension. In order to prove this result we consider sequenceentropy tuples and give their complete relation with regionallyproximal tuples.