Related papers: Singularity exchange at the frontier of the space
We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain…
We survey some recent results concerning the behaviour of the contact structure defined on the boundary of a complex isolated hypersurface singularity or on the boundary at infinity of a complex polynomial.
We study a boundary value elliptic problem having a lower order nonlinear term with subquadratic growth in the gradient of the solution and possibly singular when the solution vanishes. If the singularity is mild enough (and even in the…
The process of interaction between nonlinear waves on a free surface of a nonconducting fluid in a strong tangential electric field is simulated numerically (effects of the force of gravity and capillarity are neglected). It is shown that…
Topological singularities are ubiquitous in many areas of physics. Polarization singularities are locations at which an aspect of the polarization ellipse of light becomes undetermined or degenerate. At C points the orientation of the…
Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature…
A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
Defects or junctions in materials serve as a source of interactions for particles, and in idealized limits they may be treated as singular points yielding contact interactions. In quantum mechanics, these singularities accommodate an…
The reliability is of the most importance when employing a numerical method to solve the eigenvalue integral equations. In this paper, we present one type of particular singularities (pseudosingularities) existing in eigenvalue integral…
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…
We study the topology of some simple infinite dimensional singularities arising from spaces of \emph{algebraic formal loops}. We prove that in some simple cases the natural analogue of nearby cycles cohomology for a function on the loop…
We show how changes in unitarity-preserving boundary conditions allow continuous interpolation among the Hilbert spaces of quantum mechanics on topologically distinct manifolds. We present several examples, including a computation of…
We discuss the problem of singularity crossing in isotropic and anisotropic universes. We study at which conditions singularities can disappear in quantum cosmology and how quantum particles behave in the vicinity of singularities. Some…
The phenomenological theory revealing the generic effects of the problem symmetry, its violation, and energy conservation law on the singularities of the Poynting vector field is presented. The bifurcation scenario of their formation…
A sufficient condition for a substitution automorphism to have pure singular spectrum is given in terms of the top Lyapunov exponent of the associated spectral cocycle. As a corollary, singularity of the spectrum is established for an…
We present numerical evidence that singularities form in finite time during the evolution of 2+1 wave maps from spherically equivariant initial data of sufficient energy.
Entanglement appears under two different forms in quantum theory, namely as a property of states of joint systems and as a property of measurement eigenstates in joint measurements. By combining these two aspects of entanglement, it is…
We show that minimal shifts with zero topological entropy are topologically conjugate to interval exchange transformations, generally infinite. When these shifts have linear factor complexity (linear block growth), the conjugate interval…
Lyapunov equations with low-rank right-hand sides often have solutions whose singular values decay rapidly, enabling iterative methods that produce low-rank approximate solutions. All previously known bounds on this decay involve quantities…