Related papers: Measure theory through dynamical eyes
The article outlines in memoriam Prof. Pavel Zampa's concepts of system theory which enable to devise a measurement in dynamic systems independently of the particular system behaviour. From the point of view of Zampa's theory, terms like…
Measurement theory is the cornerstone of science, but no equivalent theory underpins the huge volumes of non-numerical data now being generated. In this study, we show that replacing numbers with alternative mathematical models, such as…
Lecture notes as per the title. In the first part, the concepts of a measurable space, measurable maps between measurable spaces and that of a measure on a measurable space are introduced, after which the fundamentals of the theory of…
These notes deal with metric spaces, Hausdorff measures and dimensions, Lipschitz mappings, and related topics. The reader is assumed to have some familiarity with basic analysis, which is also reviewed.
Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry, and partly from…
There is studied an invariant measure structure of a class of ergodicl discrete dynamical systems by means of the measure generating function method
We consider both geometric and measure-theoretic shrinking targets for ergodic maps, investigating when they are visible or invisible. Some Baire category theorems are proved, and particular constructions are given when the underlying map…
These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.
These are expanded lecture notes for the summer school on Berkovich spaces that took place at the Institut de Math\'ematiques de Jussieu, Paris in 2010. They serve to illustrate some techniques and results from the dynamics on…
This thesis is about conceptual aspects of gauge theories. Gauge theories lie at the heart of modern physics: in particular, they constitute the standard model of particle physics. At its simplest, the idea of gauge is that nature is best…
Many features of real granular fluids under rapid flow are exhibited as well by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply standard methods of kinetic theory and hydrodynamics to…
Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in [V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems,…
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…
We present numerical support for the hypothesis that macroscopic observables of dense granular media can be evaluated from averages over typical blocked configurations: we construct the corresponding measure for a class of…
Simple physical models of a measuring rod and of a clock are used to demonstrate the contraction of objects and clock retardation in special relativity. It is argued that the models could help in promoting student understanding of special…
This is a set of lectures given at the 99' Cargese Summer School: Particle Physics : Ideas and Recent Developments. They contain a pedestrian exposition of recent theoretical progress in non-perturbative field theory and string theory based…
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
This manuscript contains the lecture notes of the short courses given by one of us (F.Z.) at the summer school "Fundamental Problems in Statistical Physics XV", held in Brunico, Italy, in July 2021, and, just before that, at the summer…
We introduce a concept of porosity for measures and study relations between dimensions and porosities for two classes of measures: measures on $R^n$ which satisfy the doubling condition and strongly porous measures on $R$.
A technique of dynamically defined measures is developed and its relation to the theory of equilibrium states is shown. The technique uses Caratheodory's method and the outer measure introduced in (I. Werner, Math. Proc. Camb. Phil. Soc.…