Karlsruhe

This chapter charts the Federal Constitutional Court’s historical development, with a nuanced attention to the motley preconditions—and the irreducible contingency—of its remarkable rise. It begins with the rise of the Court, which adroitly used the opportunities offered by the uncharted situation of postwar West Germany. Especially by way of its extensive human rights jurisprudence, the Court worked toward a fundamental liberalization of the German legal system and shook up the traditional judiciary. The Federal Constitutional Court thus became the midwife of the second German democracy. However, owing to its successes and the eventual stability and prosperity of the Federal Republic, which was now a liberal society with a solidified democratic culture, the country came to depend less and less on the Court and its initiatives. The Court thus became a victim of its own success. Other factors involved in the Court’s fading importance are the loss of charisma through routinization and the increasing Europeanization and internationalization of the German legal system.

Eventually stable rational functions

For a field [Formula: see text], rational function [Formula: see text] of degree at least two, and [Formula: see text], we study the polynomials in [Formula: see text] whose roots are given by the solutions in [Formula: see text] to [Formula: see text], where [Formula: see text] denotes the [Formula: see text]th iterate of [Formula: see text]. When the number of irreducible factors of these polynomials stabilizes as [Formula: see text] grows, the pair [Formula: see text] is called eventually stable over [Formula: see text]. We conjecture that [Formula: see text] is eventually stable over [Formula: see text] when [Formula: see text] is any global field and [Formula: see text] is any point not periodic under [Formula: see text] (an additional non-isotriviality hypothesis is necessary in the function field case). We prove the conjecture when [Formula: see text] has a discrete valuation for which (1) [Formula: see text] has good reduction and (2) [Formula: see text] acts bijectively on all finite residue extensions. As a corollary, we prove for these maps a conjecture of Sookdeo on the finiteness of [Formula: see text]-integral points in backward orbits. We also give several characterizations of eventual stability in terms of natural finiteness conditions, and survey previous work on the phenomenon.

EVENTUAL STABILITY AND EVENTUAL BOUNDEDNESS FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH “SUPREMUM”

Eventual stability and eventual boundedness for nonlinear impulsive differential equations with supremums are studied. The impulses take place at fixed moments of time. Piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.