Related papers: Nonuniform Markov geometric measures
We present the main concepts and results for Graph Directed Markov Systems that have a finitely irreducible incidence matrix. We then see how these results change when the incidence matrix is not assumed to be finitely irreducible.
We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with…
The regularity of systolically extremal surfaces is a notoriously difficult problem already discussed by M. Gromov in 1983, who proposed an argument toward the existence of $L^2$-extremizers exploiting the theory of $r$-regularity developed…
Mean Hausdorff dimension is a dynamical version of Hausdorff dimension. It provides a way to dynamicalize geometric measure theory. We pick up the following three classical results of fractal geometry. (1) The calculation of Hausdorff…
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…
We define an infinite graded graph of ordered pairs and a~canonical action of the group $\mathbb{Z}$ (the adic action) and of the infinite sum of groups of order two~$\mathcal{D}=\sum_1^{\infty} \mathbb{Z}/2\mathbb{Z}$ on the path space of…
In 2007 H. Long-Guang and Z. Xian, [H. Long-Guang and Z. Xian, Cone Metric Spaces and Fixed Point Theorems of Contractive Mapping, J. Math. Anal. Appl., 322(2007), 1468-1476], generalized the concept of a metric space, by introducing cone…
We prove a structural result for measure preserving systems naturally associated with any finite collection of multiplicative functions that take values on the complex unit disc. We show that these systems have no irrational spectrum and…
We investigate in this work some situations where it is possible to estimate or determine the upper and the lower $q$-generalized fractal dimensions $D^{\pm}_{\mu}(q)$, $q\in\mathbb{R}$, of invariant measures associated with continuous…
We extend results of parametric geometry of numbers to a general diagonal flow on the space of lattices. Moreover, we compute the Hausdorff dimension of the set of trajectories with every given behavior, with respect to a nonstandard metric…
In this paper we collect several examples of convergence of functions of random processes to generalized functionals of those processes. We remark that the limit is always finitely absolutely continuous with respect to Wiener measure. We…
We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian…
It is shown that the stochastic model of Fenyes and Nelson can be generalized in such a way that the diffusion constant of the Markov theory becomes a free parameter. This extra freedom allows one to identify quantum mechanics with a class…
We develop the formalism of universal torsors in equivariant birational geometry and apply it to produce new examples of nonbirational but stably birational actions of finite groups.
In this paper we present some new results on the existence of solutions of generalized variational inequalities in real reflexive Banach spaces with Fr\'echet differentiable norms. Moreover, we also give some theorems about the structure of…
Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…
We prove the convergence at an exponential rate towards the invariant probability measure for a class of solutions of stochastic differential equations with finite delay. This is done, in this non-Markovian setting, using the cluster…
We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant form by means of twisted equivariant cohomology of the manifold. We apply…
Zhang introduced semipositive metrics on a line bundle of a proper variety. In this paper, we generalize such metrics for a line bundle $L$ of a paracompact strictly $K$-analytic space $X$ over any non-archimedean field $K$. We prove…
Fractal measures of images of continuous maps from the set of p-adic numbers Qp into complex plane C are analyzed. Examples of "anomalous" fractals, i.e. the sets where the D-dimensional Hausdorff measures (HM) are trivial, i.e. either…