In this paper we study ergodic theory of countable Markov shifts. These are dynamical systems defined over non-compact spaces. Our main result relates the escape mass, measure theoretic entropy, and entropy at infinity system. This relation has several consequences. For example obtain that map is upper semi-continuous measures form an dense subset. results also provide new proofs describing exi...

We define the topological entropy per unit volume in parabolic PDE’s such as the complex GinzburgLandau equation, and show that it exists and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a constructive implementation of a bound on the inertial range of such equations. Using this bound, we are able to propose a finite sampling algorithm which allows ...

Let M2 be the space of quadratic rational maps f : P 1 → P , modulo the action by conjugation of the group of Möbius transformations. In this paper a compactification X of M2 is defined, as a modification of Milnor’s M 2 ' CP , by choosing representatives of a conjugacy class [f ] ∈ M2 such that the measure of maximal entropy of f has conformal barycenter at the origin in R, and taking the clos...

We define the topological entropy per unit volume in parabolic PDE's such as the complex Ginzburg-Landau equation, and show that it exists, and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a constructive implementation of a bound on the inertial range of such equations. Using this bound, we are able to propose a finite sampling algorithm which allow...

One important issue in the theory of Ordered Weighted Averaging (OWA) operators is the determination of the associated weights. One of the first approaches, suggested by O’Hagan, determines a special class of OWA operators having maximal entropy of the OWA weights for a given level of orness; algorithmically it is based on the solution of a constrained optimization problem. In this paper, using...

1. Introduction Let X be a compact metric space and T: X-> X a homeomorphism of X onto X. Let M(T) denote the collection of all T-invariant Borel probability measures on X. By Krylov and Bogolioubov's work we know M(T) is non-empty (see [10]). M{T) is a convex set and closed in the weak topology. For /x e M(T), h(T, p) will denote the measure-theoretic entropy of T with respect to p. Ifh top (T...

Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the distribution of connected components. We determine the size of the percolation cluster above the percolation threshold. The conditional degree distribution on...