861 research outputs found
Equilibrium Measures for Maps with Inducing Schemes
We introduce a class of continuous maps f of a compact metric space I
admitting inducing schemes and describe the tower constructions associated with
them. We then establish a thermodynamical formalism, i.e., describe a class of
real-valued potential functions \phi on I which admit unique equilibrium
measures \mu_\phi minimizing the free energy for a certain class of measures.
We also describe ergodic properties of equilibrium measures including decay of
correlation and the Central Limit Theorem. Our results apply in particular to
some one-dimensional unimodal and multimodal maps as well as to
multidimensional nonuniformly hyperbolic maps admitting Young's tower. Examples
of potential functions to which our theory applies include \phi_t=-t\log|df|
with t\in(t_0, t_1) for some t_0<1<t_1. In the particular case of S-unimodal
maps we show that one can choose t_0<0 and that the class of measures under
consideration comprises all invariant Borel probability measures. Thus our
results establish existence and uniqueness of both the measure of maximal
entropy (by a different method than Hofbauer) and the absolutely continuous
invariant measure extending results by Bruin and Keller for the parameters
under consideration
Affine actions of a free semigroup on the real line
We consider actions of the free semigroup with two generators on the real
line, where the generators act as affine maps, one contracting and one
expanding, with distinct fixed points. Then every orbit is dense in a
half-line, which leads to the question whether it is, in some sense, uniformly
distributed. We present answers to this question for various interpretations of
the phrase ``uniformly distributed''
A new transatlantic trade war?: Issues surrounding the US-EU steel conflict
Six months after the Doha agreement on a new round of talks to liberalise world trade, tension is mounting between the EU and the US, the world's two major trading powers, giving rise to fears of a full-blown transatlantic trade war and a new wave of global protectionism. The contributors to this Forum look at the causes of, and possible remedies for, this development, taking economic, legal and political aspects into consideratio
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