Related papers: Complexity of Coexistence Regions in the GRHT Map
Motivated by persistent homology and topological data analysis, we consider formal sums on a metric space with a distinguished subset. These formal sums, which we call persistence diagrams, have a canonical 1-parameter family of metrics…
We prove that for a generic family of circle diffeomorphisms every parameter value that corresponds to an irrational rotation number is approximated by parameter values for which the diffeomorphisms have arbitrarily large finite numbers of…
We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations containing a compact spatial heterogeneity. While one-dimensional…
A classic theorem by Steinitz states that a graph G is realizable by a convex polyhedron if and only if G is 3-connected planar. Zonohedra are an important subclass of convex polyhedra having the property that the faces of a zonohedron are…
Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an assignment that minimizes the number of unsatisfied…
Singular Hopf bifurcation occurs in generic families of vector-fields with two slow variables and one fast variable. Normal forms for this bifurcation depend upon several parameters, and the dynamics displayed by the normal forms is…
We investigate the structure of the Earth co-orbital region at low eccentricity and low inclination using a semi-analytical model of the 1:1 mean-motion resonance. The dynamics of asteroids in co-orbital motion with the Earth is described…
The closedness condition for real geodesics on n-dimensional ellipsoids is in general transcendental in the parameters (semiaxes of the ellipsoid and constants of motion). We show that it is algebraic in the parameters if and only if both…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on…
Changes in environmental or system parameters often drive major biological transitions, including ecosystem collapse, disease outbreaks, and tumor development. Analyzing the stability of steady states in dynamical systems provides critical…
While large language models (LLMs) are trained purely on textual data, prior work has shown that their internal representations can exhibit rich geometric structure in embedding space. Building on this line of work, we investigate whether…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
We consider systems made of autonomous mobile robots evolving in highly dynamic discrete environment i.e., graphs where edges may appear and disappear unpredictably without any recurrence, stability, nor periodicity assumption. Robots are…
The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples include reversible maps with symmetry lines. The present work…
This article concerns arbitrary finite heteroclinic networks in any phase space dimension whose vertices can be a random mixture of equilibria and periodic orbits. In addition, tangencies in the intersection of un/stable manifolds are…
Triangles are abundant in real-world networks but rare in standard null models for sparse graphs. Existing explanations typically rely on explicit triadic closure mechanisms or geometry-based connection rules. We propose an alternative…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
Here we consider isofrequency pairing of geodesic orbits that share the same three orbital frequencies associated with $\Omega^{\hat{r}}$, $\Omega^{\hat{\varphi}}$, and $\Omega^{\hat{\omega}}$ in a particular region of parameter space…
The discovery of binary and triple asteroids in addition to the execution of space missions to minor celestial bodies in the past several years have focused increasing attention on periodic orbits around irregular-shaped celestial bodies.…