Related papers: Finitary Codes, a short survey
We provide an effective classification of postcritically finite polynomials as dynamical systems by means of Hubbard Trees. This can be viewed as an application of the results developed in part 1 (Stony Brook IMS 1993/5).
The dynamical system approach has recently acquired great importance in the investigation on higher order theories of gravity. In this talk I review the main results and I give brief comments on the perspectives for further developments.
The aim of this work is to offer a family of invariants that allows us to classify finite potent endomorphisms on arbitrary vector spaces, generalizing the classification of endomorphisms on finite-dimensional vector spaces. As a particular…
A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. Keywords: Weil representation,…
An S-adic system is a symbolic dynamical system generated by iterating an infinite sequence of substitutions or morphisms, called a directive sequence. A finitary S-adic dynamical system is one where the directive sequence consists of…
In the given paper we consider finite difference approximations to systems of polynomially-nonlinear partial differential equations whose coefficients are rational functions over rationals in the independent variables. The notion of strong…
Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many…
The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…
We prove some results on the border of Ramsey theory (finite partition calculus) and model theory. Also a beginning of classification theory of finite models in undertaken.
We state necessary and sufficient conditions to uniquely identify (modulo state isomorphism) a linear time-invariant minimal input-state-output system from finite input-output data and upper- and lower bounds on lag and state space…
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…
Rare trajectories of stochastic systems are important to understand -- because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their…
I review a number of cognate issues that, taken together, pertain to the creation of a non-reductionistic theory of multiscale coordination and present one candidate theory based on the principle of dynamical similarity.
Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…
We survey some recent results in Ramsey theory. We indicate their connections with topological dynamics. On the foundational side, we describe an abstract approach to finite Ramsey theory. We give one new application of the abstract…
We approximate a chain recurrent dynamical system by periodic dynamical systems. This is similar to the well known Bohr theorem on approximation of almost periodic functions by periodic functions.