Buildings , extensions , and volume growth entropy
نویسندگان
چکیده
Let F be a non-Archimedean local field and let E be a finite extension of F . Let G be an F -split semisimple F -group. We discuss how to compare volumes on the Bruhat–Tits buildings BE and BF of G(E) and G(F ) respectively.
منابع مشابه
Entropy of infinite systems and transformations
The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...
متن کاملEntropy of Hyperbolic Buildings
We characterize the volume entropy of a regular building as the topological pressure of the geodesic flow on an apartment. We show that the entropy maximizing measure is not Liouville measure for any regular hyperbolic building. As a consequence, we obtain a strict lower bound on the volume entropy in terms of the branching numbers and the volume of the boundary polyhedrons.
متن کاملSome properties of the parametric relative operator entropy
The notion of entropy was introduced by Clausius in 1850, and some of the main steps towards the consolidation of the concept were taken by Boltzmann and Gibbs. Since then several extensions and reformulations have been developed in various disciplines with motivations and applications in different subjects, such as statistical mechanics, information theory, and dynamical systems. Fujii and Kam...
متن کاملVolume Growth, Entropy and the Geodesic Stretch
Let (M, g) be a compact Riemannian manifold with universal covering M̃ . The simplest asymptotic invariant which can be associated to (M, g) is the exponential growth rate h(g) of volume on the universal covering, called the volume entropy. If B r (p) denotes the geodesic ball of radius r about p ∈ M̃ and volg(B r (p)) describes its volume with respect to the Riemannian metric g lifted to M̃ then ...
متن کاملFlow field, heat transfer and entropy generation of nanofluid in a microchannel using the finite volume method
In this study, the finite volume method and the SIMPLER algorithm is employed to investigate forced convection and entropy generation of Cu-water nanofluid in a parallel plate microchannel. There are four obstacles through the microchannel, and the slip velocity and temperature jump boundary conditions are considered in the governing equations to increase the accuracy of modeling. The study is ...
متن کامل