Related papers: Bifurcations of unimodal maps
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
This is a lightning introduction to some modern techniques used in the study of the statistical properties of hyperbolic dynamical systems. The emphasis is not in presenting a comprehensive theory but rather in fleshing out the main ideas…
Understanding traffic statics and dynamics in urban networks is critical to develop effective control and management strategies. In this paper, we provide a novel approach to study the traffic statics and dynamics in a signalized…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…
Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…
We show the existence of polynomial maps which have a regular bifurcation value, while over a neighbourhood of this value the fibres are connected and diffeomorphic.
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…
The existence of translated curves for quasiperiodically forced maps is established, under very mild regularity hypotheses, for rotation numbers of constant type. Among the translated curves, the invariant curves are characterized as the…
Homeomorphisms allowing us to prove topological equivalences between one-parameter families of maps undergoing the same bifurcation are constructed in this paper. This provides a solution for a classical problem in bifurcation theory that…
A random number of items each independently marked with one of a collection of colours gives rise to the multinomial marking, which generalises binomial thinning. A multivariate version, where previously marked items are then re-marked, has…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
Retraction maps have been generalized to discretization maps in (Barbero Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as…
Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps…
This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…
We focus on an interpolation method referred to Bayesian reconstruction in this paper. Whereas in standard interpolation methods missing data are interpolated deterministically, in Bayesian reconstruction, missing data are interpolated…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
In this study, we challenge the traditional approach of frequency analysis on directed graphs, which typically relies on a single measure of signal variation such as total variation. We argue that the inherent directionality in directed…
We outline the proofs of several principal statements in conventional renormalization theory. This may be of some use in the light of new trends and new techniques (Hopf algebras, etc.) recently introduced in the field.