Related papers: Dynamical height growth: left, right, and total or…
The Galois theory of logarithmic differential equations with respect to relative D-groups in partial differential-algebraic geometry is developed.
We prove a general multi-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers…
Complex systems have motivated continuing interest from the scientific community, leading to new concepts and methods. Growing systems represent a case of particular interest, as their topological, geometrical, and also dynamical properties…
We study the dynamics of synthetic molecules whose architectures are generated by space transformations from a point group acting on seed resonators. We show that the dynamical matrix of any such molecule can be reproduced as the left…
In this work we are going to study the dynamics of the linear automorphisms of a measure convolution algebra over a finite group, $T(\mu)=\nu * \mu$. In order to understand an classify the asymptotic behavior of this dynamical system we…
We generalize the two dimensional Lozi map in order to systematically obtain piece-wise continuous maps in three and higher dimensions. Similar to higher-dimensional generalizations of the related Henon map, these higher-dimensional Lozi…
Let K/k be a finite Galois extension of number fields with Galois group G, S a large set of primes of K, and E the G-module of S-units of K. Previous work has determined the data which is necessary to determine the stable isomorphism class…
A model of discrete spacetime on a microscopic level is considered. It is a directed acyclic dyadic graph. This is the particular case of a causal set. The goal of this model is to describe particles as some repetitive symmetrical…
Let G denote a closed, connected, self adjoint, noncompact subgroup of GL(n,R), and let d_{R} denote the canonical right invariant Riemannian metric on G. For v in R^{n} let G_{v} = {g in G : g(v) = v}. We obtain algebraically defined upper…
We study the component structure of the random graph $G=G_{n,m,d}$. Here $d=O(1)$ and $G$ is sampled uniformly from ${\mathcal G}_{n,m,d}$, the set of graphs with vertex set $[n]$, $m$ edges and maximum degree at most $d$. If $m=\mu n/2$…
We study the dynamical properties of a large class of rational maps with exactly three ramification points. By constructing families of such maps, we obtain infinitely many conservative maps of degree $d$; this answers a question of…
Let $\phi$ be a post-critically finite branched covering of a two-sphere. By work of Koch, the Thurston pullback map induced by $\phi$ on Teichm\"{u}ller space descends to a multi-valued self-map --- a Hurwitz correspondence…
A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…
There is a deep and interesting connection between the topological properties of a graph and the behaviour of the dynamical system defined on it. We analyse various kind of graphs, with different contrasting connectivity or degree…
Predicting dynamic behaviors is one of the goals of science in general as well as essential to many specific applications of human knowledge to real world systems. Here we introduce an analytic approach using the sigmoid growth curve to…
This article proposes a novel methodology to learn a stable robot control law driven by dynamical systems. The methodology requires a single demonstration and can deduce a stable dynamics in arbitrary high dimensions. The method relies on…
The decimal expansion real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history…
We study the zero sets of the independence polynomial on recursive sequences of graphs. We prove that for a maximally independent starting graph and a stable and expanding recursion algorithm, the zeros of the independence polynomial are…
L\"uroth's theorem describes the dominant maps from rational curves over a field. In this note we study those dominant rational maps from cartesian powers $X^{\Psi}$ of geometrically irreducible varieties $X$ over a field $k$ for infinite…
Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The…