Related papers: Th\'eor\`emes d'\'equidistribution pour les syst\`…
For every $m\in\mathbb{N}$, we establish the equidistribution of the sequence of the averaged pull-backs of a Dirac measure at any given value in $\mathbb{C}\setminus\{0\}$ under the $m$-th order derivatives of the iterates of a polynomials…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
This work is devoted to the study of the relationships between graph theory and the qualitative analysis of ordinary differential equations, with a special focus on two-dimensional systems. In particular, we reinterpret classical results…
We draw a connection between the model-theoretic notions of modularity (or one-basedness), orthogonality and internality, as applied to difference fields, and questions of descent in in algebraic dynamics. In particular we prove in any…
This article has one single purpose: introduce a new and simple, yet highly insightful approach to capture, fully and quantitatively, the dynamics of the circular flow of income in economies. The proposed approach relies mostly on basic…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
In the present article, we define a notion of good height functions on quasi-projective varieties $V$ defined over number fields and prove an equidistribution theorem of small points for such height functions. Those good height functions…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
We consider an independently identically distributed random dynamical system generated by finitely many, non-uniformly expanding Markov interval maps with a finite number of branches. Assuming a topologically mixing condition and the…
A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…
The paper deals with the study of labor market dynamics, and aims to characterize its equilibriums and possible trajectories. The theoretical background is the theory of the segmented labor market. The main idea is that this theory is well…
The aim of this note is to recast somewhat informal axiom system of quantum mechanics used by physicists (Dirac calculus) in the language of Continuous Logic. We note an analogy between Tarski's notion of cylindric algebras, as a tool of…
In this paper we provide a detailed study on effective versions of the celebrated Bilu's equidistribution theorem for Galois orbits of sequences of points of small height in the $N$-dimensional algebraic torus, identifying the quantitative…
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…
Let X be a projective integral normal scheme over a number field F; let L be a ample line bundle on X together with a semi-positive adelic metric in the sense of Zhang. The main results of this article are 1) A formula which computes the…
We propose generalized Fermat's conjecture in the framework of arithmetic dynamics, and give evidences. The multi-indexed version is added.
The dynamics of distributed sources is described by nonlinear partial differential equations. Lagrangian analytical solutions of these (and associated) equations are obtained and discussed in the context of Lagrangian modeling - from the…
The essential minimum and equidistribution of small points are two well-established interrelated subjects in arithmetic geometry. However, there is lack of an analogue of essential minimum dealing with higher dimensional subvarieties, and…
We study Birkhoff sums as distributions. We obtain regularity results on such distributions for various dynamical systems with hyperbolicity, as hyperbolic linear maps on the torus and piecewise expanding maps on the interval. We also give…