In this paper, we study a class of quasi-invariant measures on paths generated by discrete dynamical systems. Our main result characterizes the subfamily of these measures which admit a certain desintegration. This is a desintegration with respect to a random walk Markov process which is indexed by the starting point of the paths. Our applications include wavelet constructions on Julia sets of ...

Article ID: WMC004271 Article Type: Guidelines Submitted on:07-Jun-2013, 04:41:04 AM GMT Published on: 07-Jun-2013, 08:15:41 AM GMT Article URL: http://www.webmedcentral.com/article_view/4271 Subject Categories:NEUROSURGERY

In this paper, we study a class of quasi-invariant measures on paths generated by discrete dynamical systems. Our main result characterizes the subfamily of these measures which admit a certain disintegration. This is a disintegration with respect to a random walk Markov process which is indexed by the starting point of the paths. Our applications include wavelet constructions on Julia sets of ...

The aim of this short lecture course is to develop Selberg's trace formula for a compact hyperbolic surface M, and discuss some of its applications. The main motivation for our studies is quantum chaos: the Laplace-Beltrami operator −∆ on the surface M represents the quantum Hamiltonian of a particle, whose classical dynamics is governed by the (strongly chaotic) geodesic flow on the unit tange...

Quantum affine reflection algebras are coideal subalgebras of quantum affine algebras that lead to trigonometric reflection matrices (solutions of the boundary Yang-Baxter equation). In this paper we use the quantum affine reflection algebras of type d (1) n to determine new n-parameter families of non-diagonal reflection matrices. These matrices describe the reflection of vector solitons off t...

The first examples of complete projective connections are uncovered: on surfaces, normal projective connections whose geodesics are all closed and embedded are complete. On manifolds of any dimension, normal projective connections induced from complete affine connections with slowly decaying positive Ricci curvature are complete.

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

In this paper, we study modular forms on two simply connected groups of type D4 over Q. One group, Gs, is a globally split group of type D4, viewed as the group of isotopies of the split rational octonions. The other, Gc, is the isotopy group of the rational (non-split) octonions. We study automorphic forms on Gs in analogy to the work of Gross, Gan, and Savin on G2; namely we study automorphic...

b∈B μ ◦σ b . There are two a priori candidates for an associated orthogonal harmonic analysis : (i) the existence of some subset Λ in R such that the exponentials {e}λ∈Λ form an orthogonal basis for L (μ); and (ii) the existence of a certain dual pair of representations of the C-algebra ON where N is the cardinality of the set B. (For each N , the C-algebra ON is known to be simple; it is also ...