Aug 2026· International Journal of Analysis and Applications· Vol 24, pp. 267· 0 citations· 26 references
Abstract
Within the scope of the qualitative study of dynamical systems via graph-based methods, we extend the notion of structural graph to dynamical systems generated by actions of monoids, as abstract algebraic structures. The setting considers the action of an ordered monoid (not necessarily \(\mathbb{N},\ \mathbb{Z}\) or \(\mathbb{R}\)) on a metric space in a general sense, and therefore includes a wider class of dynamical systems than those described solely by ordinary differential or difference equations. We then investigate several fundamental properties of the structural graph, such as connectedness and degeneracy. In particular, it is shown that in the finite case, the structural graph associated to a \(C^{1}\)-vector field on a closed differential manifold is necessarily connected. As illustrative examples, we consider the classical van der Pol oscillator on the Poincaré sphere, the mathematical pendulum on the phase plane and the nonanalytic case of the center-focus. And as a perspective, we suggest work about what could be considered as a new form of linearization of dynamical systems via their structural graph, and address the question about a possible use for investigating global qualitative properties such as structural stability.
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviours. If the conditions are ideal and the number of observations is sufficient, we can represent these phenomena by a dynamical system, also called a functional digraph, that is to say a graph where each n...
M. Gadouleau, Sara Riva, Marius Rolland et al.· 0 citations
We study the stationary focusing nonlinear Schr\"odinger equation on the product $\mathbb{R}^N \times \mathcal{G}$ of the Euclidean space with a compact metric graph, in the mass-constrained variational setting. Such a product is a hybrid structure of a new type: all its faces are $(N+1)$-dimensional and are glued alon...
Nicola Soave, G. Verzini, Lorenzo Villata· 0 citations
Since the 1980s, the Bogomolov multiplier of a finite group has been known to obstruct rationality in complex algebraic geometry, and more recently it is understood to be responsible for any torsion in the oriented and stable unitary 2-dimensional $G$-equivariant bordism groups $\Omega_2^{SO,G}$ and $\Omega_2^{U,G}$. I...
The zero-divisor graph of a commutative ring provides a natural connection between algebraic and graph-theoretic structures. Although extensive research has been conducted on the algebraic and combinatorial properties of zero-divisor graphs, their connectivity and metric properties over finite semilocal rings remain co...
Presley Kiplagat· Earthline Journal of Mathema...· 0 citations
We propose a holonomy-based framework for discretizing curvature on graphs equipped with local symmetric positive-definite metrics. Each vertex carries a fibre metric \(g_i\), and each directed edge carries a reversible metric-compatible transport \(F_{ij}\). The ordered product around an oriented triangular loop \(\ma...
We develop a framework for studying discrete subgroups of $\mathsf{PGL}(d+1,\mathbb{R})$ via the paracomplex hyperbolic space $\mathbb{H}_\tau^d$, a rank-$1$ pseudo-Riemannian symmetric space. We characterize projective transverse, relatively Anosov, and Anosov subgroups in terms of properly discontinuous, geometricall...
