Related papers: Universal models for Lorenz maps

To each graph on $n$ vertices there is an associated subspace of the $n \times n$ matrices called the operator system of the graph. We prove that two graphs are isomorphic if and only if their corresponding operator systems are unitally…

Dynamics arising persistently in smooth dynamical systems ranges from regular dynamics (periodic, quasiperiodic) to strongly chaotic dynamics (Anosov, uniformly hyperbolic, nonuniformly hyperbolic modelled by Young towers). The latter…

Various problems of geometry, topology and dynamical systems on surfaces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a flat metric with several cone-type…

A new family of maximal curves over a finite field is presented and some of their properties are investigated.

The simple realistic model of the tippe top is considered. An averaged system of equations of motion is obtained in special evolutionary variables. Through the qualitative analysis of this system the general features of the motion of the…

In this paper, we learn dynamics models for parametrized families of dynamical systems with varying properties. The dynamics models are formulated as stochastic processes conditioned on a latent context variable which is inferred from…

We show that there is a logarithmic algebraic space parameterizing logarithmic morphisms between fixed logarithmic schemes when those logarithmic schemes satisfy natural hypotheses. As a corollary, we obtain the algebraicity of the stack of…

This is a review of [Michor, Peter W.: The moment mapping for a unitary representation, Ann. Global Anal. Geometry, 8, No 3(1990), 299--313] including a careful description of calculus in infinite dimensions. For any unitary representation…

A map which is non-orientable or has non-empty boundary has a canonical double cover which is orientable and has empty boundary. The map is called stable if every automorphism of this cover is a lift of an automorphism of the map. This note…

We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…

The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions, such as when there is some sparsity…

The Lang map, namely the universal dominant rational map to a variety of general type, is constructed and briefly discussed in relation with arithmetic conjectures of Harris, Lang and Manin. Existence of the Lang map follows from the…

In the present paper, we prove the existence of universal polynomials which express multi-singularity loci classes of prescribed types for proper morphisms between smooth schemes over an algebraically closed field of characteristic zero --…

One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams. Despite much effort, this is still largely an open problem. In this paper, we present a series of…

A regular map is a surface together with an embedded graph, having properties similar to those of the surface and graph of a platonic solid. We analyze regular maps with reflection symmetry and a graph of density strictly exceeding 1/2, and…

A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all…

A generalized Lyapunov method is outlined which predicts global stability of a broad class of dissipative dynamical systems. The method is applied to the complex Lorenz model and to the Navier-Stokes equations. In both cases one finds…

A family of mappings is called uniformly light if the image of the continuum under these mappings cannot be contracted to a point under the sequence of mappings of the family. In this paper, we are interested in the problem of the uniform…

Tables of the currently known parameters of symmetric configurations are given. Formulas for parameters of the known infinite families of symmetric configurations are presented as well. The results of the recent paper [18] are used. This…

We present a simple model of network dynamics that can be solved analytically for uniform networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random…