Related papers: A catalogue of singularities
The term boundary crisis refers to the destruction or creation of a chaotic attractor when parameters vary. The locus of a boundary crisis may contain regions of positive Lebesgue measure marking the transition from regular dynamics to the…
In this paper, a system of one-dimensional gas dynamics equations is considered. This system is a particular case of Jacobi type systems and has a natural representation in terms of 2-forms on 0-jet space. We use this observation to find a…
The behaviour of a solid-liquid-gas system near the three-phase contact line is considered using a diffuse-interface model with no-slip at the solid and where the fluid phase is specified by a continuous density field. Relaxation of the…
The line bundle mean curvature flow is a complex analogue of the mean curvature flow for Lagrangian graphs, with fixed points solving the deformed Hermitian-Yang-Mills equation. In this paper we construct two distinct examples of…
The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…
We consider fixed-point equations for probability distributions on isometry classes of measured metric spaces. The construction is required to be recursive and tree-like, but we allow loops for the geodesics between points in the support of…
We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
In this work, we study the dynamical systems analysis of phantom dark energy models considering a general potential. The stability analysis of the system shows that there is only one fixed point which could be the beginning of the universe…
The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our…
We classify all possible singularities in the electronic dispersion of two-dimensional systems that occur when the Fermi surface changes topology, using catastrophe theory. For systems with up to seven control parameters (i.e., pressure,…
We study singularity confinement phenomena in examples of delay-differential Painlev\'e equations, which involve shifts and derivatives with respect to a single independent variable. We propose a geometric interpretation of our results in…
Point vortex models are presented for the generalized Euler equations, which are characterized by a fractional Laplacian relation between the active scalar and the streamfunction. Special focus is given to the case of the surface…
The origin of spectral singularities in finite-gap singly periodic PT-symmetric quantum systems is investigated. We show that they emerge from a limit of band-edge states in a doubly periodic finite gap system when the imaginary period…
It is revealed that distribution functions of practical gases relate to singularities and such singularities can, with molecular motion, spread to the entire region of interest. It is also shown that even common continuous distribution…
We search for acoustic analogues of a spherical symmetric black hole with a pointlike source. We show that the gravitational system has a dynamical counterpart in the constrained, steady motion of a fluid with a planar source. The equations…
In this article we study how bad can be the singularities of a time-optimal trajectory of a generic control affine system. In the case where the control is scalar and belongs to a closed interval it was recently shown in [6] that…
This is the first of two papers devoted to the study of the properties of the blow-up surface for the $N$ dimensional semilinear wave equation with subconformal power nonlinearity. In a series of papers, we have clarified the situation in…
We introduce a method of rigorous analysis of the location and type of complex singularities for nonlinear higher order PDEs as a function of the initial data. The method is applied to determine rigorously the asymptotic structure of…
We consider the dynamics of lattices which have constrained constitutive units flexible in only their mutual orientations. A continuum description is derived through which it is shown that the models have zero shear velocity, free-particle…