Some remarks on modified power entropy

The aim of this note is to point out some observations concerning modified power entropy of $\Z$- and $\N$-actions. First, we provide an elementary example showing that this quantity is sensitive to transient dynamics, and therefore does not satisfy a variational principle. Further, we show that modified power entropy is not suitable to detect the break of equicontinuity which takes place during the transition from almost periodic to almost automorphic minimal systems. In this respect, it differs from power entropy and amorphic complexity, which are two further topological invariants for zero entropy systems (`slow entropies'). Finally, we construct an example of an irregular Toeplitz flow with zero modified power entropy.Comment: 17 pages, to appear in AMS Contemporary Mathematics serie

Coupled skinny baker's maps and the Kaplan-Yorke conjecture

The Kaplan-Yorke conjecture states that for "typical" dynamical systems with a physical measure, the information dimension and the Lyapunov dimension coincide. We explore this conjecture in a neighborhood of a system for which the two dimensions do not coincide because the system consists of two uncoupled subsystems. We are interested in whether coupling "typically" restores the equality of the dimensions. The particular subsystems we consider are skinny baker's maps, and we consider uni-directional coupling. For coupling in one of the possible directions, we prove that the dimensions coincide for a prevalent set of coupling functions, but for coupling in the other direction we show that the dimensions remain unequal for all coupling functions. We conjecture that the dimensions prevalently coincide for bi-directional coupling. On the other hand, we conjecture that the phenomenon we observe for a particular class of systems with uni-directional coupling, where the information and Lyapunov dimensions differ robustly, occurs more generally for many classes of uni-directionally coupled systems (also called skew-product systems) in higher dimensions.Comment: 33 pages, 3 figure

The German-Czech Border Region after the Fall of the Iron Curtain : Effects on the Labour Market

Using the IAB Employment Sample (IABS) covering 1980-2001 we investigate what impact the fall of the Iron Curtain has had on the skill structure of employment and wages in the western German districts neighbouring the Czech Republic. The introduction of free trade in this region, which has one of the world´s largest spatial wage differentials, can be seen as a natural experiment. We presume that changes in skill and wage structures are particularly apparent in the regions situated immediately on the open border. Distinguishing three skill categories we obtain unexpected results. Though we observe a general shift from low-skilled jobs towards skilled jobs and a convergence trend of border regions towards the national average, we do not find a special effect for the period after the opening of the border, neither concerning the skill structure nor the wage differentials. -- Unter Verwendung von Daten der IAB-Regionalstichprobe (IABS) untersuchen wir, ob nach dem Fall des Eisernen Vorhangs Qualifizierungstrends und Lohnentwicklung in den bayerischen Grenzregionen zu Tschechien signifikante Unterschiede im Vergleich mit der Entwicklung auf aggregierter staatlicher Ebene aufweisen. Der Trend zu höherer Qualifizierung sowie der Trend zu höheren relativen Löhnen für besser Qualifizierte sollten dort überdurchschnittlich messbar sein. Unsere Resultate können einen speziellen Grenzöffnungseffekt jedoch weder bei der Qualifikationsstruktur noch bei der relativen Lohnentwicklung in der Grenzregion feststellen.border regions,international trade,employment,wage inequality

The German-Czech border region after the fall of the Iron Curtain: Effects on the labour market : an empirical study using the IAB Employment Sample (IABS)

"Using the IAB Employment Sample (IABS) covering 1980-2001 we investigate what impact the fall of the Iron Curtain has had on the skill structure of employment and wages in the western German districts neighbouring the Czech Republic. The introduction of free trade in this region, which has one of the world's largest spatial wage differentials, can be seen as a natural experiment. We presume that changes in skill and wage structures are particularly apparent in the regions situated immediately on the open border. Distinguishing three skill categories we obtain unexpected results. Though we observe a general shift from low-skilled jobs towards skilled jobs and a convergence trend of border regions towards the national average, we do not find a special effect for the period after the opening of the border, neither concerning the skill structure nor the wage differentials." (Author's abstract, IAB-Doku) ((en))Grenzgebiet, Qualifikationsstruktur, Lohnhöhe, osteuropäischer Transformationsprozess - Auswirkungen, IAB-Beschäftigtenstichprobe, Bayern, Tschechische Republik, Bundesrepublik Deutschland

Thermodynamic formalism for transient dynamics on the real line

We develop a new thermodynamic formalism to investigate the transient behaviour of maps on the real line which are skew-periodic $\mathbb{Z}$-extensions of expanding interval maps. Our main focus lies in the dimensional analysis of the recurrent and transient sets as well as in determining the whole dimension spectrum with respect to $\alpha$-escaping sets. Our results provide a one-dimensional model for the phenomenon of a dimension gap occurring for limit sets of Kleinian groups. In particular, we show that a dimension gap occurs if and only if we have non-zero drift and we are able to precisely quantify its width as an application of our new formalism.Comment: 23 pages, 5 figure