Abstract. The purpose of this paper is to present a weighted kneading theory for unidimensional maps with holes. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with holes and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy, the Hausdorff dimension and the ...

The notion of topological entropy dimension for a Z-action has been introduced to measure the subexponential complexity of zero entropy systems. Given a Z2-action, along with a Z2-entropy dimension, we also consider a finer notion of directional entropy dimension arising from its subactions. The entropy dimension of a Z2-action and the directional entropy dimensions of its subactions satisfy ce...

Let (X, d) be a compact metric space, f : X 7→ X be a continuous map satisfying a property we call almost specification (which is slightly weaker than the g-almost product property of Pfister and Sullivan), and φ : X 7→ R be a continuous function. We show that the set of points for which the Birkhoff average of φ does not exist (which we call the irregular set) is either empty or has full topol...

Let (X, d) be a compact metric space, f : X 7→ X be a continuous map satisfying a property we call almost specification (which is slightly weaker than the g-almost product property of Pfister and Sullivan), and φ : X 7→ R be a continuous function. We show that the set of points for which the Birkhoff average of φ does not exist (which we call the irregular set) is either empty or has full topol...

As a point of departure it is suggested that Quantum Cosmology is a topo-logical concept independent from metrical constraints. Methods of continuous topological evolution and topological thermodynamics are used to construct a cosmological model of the present universe, using the techniques based upon Car-tan's theory of exterior differential systems. Thermodynamic domains, which are either Ope...