Search results for " singularity"

On the number of singularities of a generic surface with boundary in a 3-manifold

1998

Convergent transformations into a normal form in analytic Hamiltonian systems with two degrees of freedom on the zero energy surface near degenerate …

2004

We study an analytic Hamiltonian system with two degrees of freedom, having the origin as an elliptic singularity. We assume that the full Birkhoff normal form exists and is divisible by its quadratic part, being indefinite. We show that under the Bruno condition and under the restriction to the zero energy surface, a real analytic transformation into a normal form exists. Such a normal form coincides with the restriction of the Birkhoff normal form to the zero energy surface up to an order as large as we want.

On stability of generic subriemannian caustic in the three-space

2000

Abstract The singularities of exponential mappings in subriemannian geometry are interesting objects, that are already non-trivial at the local level, contrarily to their Riemannian analogs. The simplest case is the three-dimensional contact case. Here we show that the corresponding generic caustics have moduli at the origin, and the first module that occurs has a simple geometric interpretation. On the contrary, we prove a stability result of the “big wave front”, that is, of the graph of the multivalued arclength function, reparametrized in a certain way. This object is a three-dimensional surface, which has also the natural structure of a wave front. The projection on the three-dimension…

Tree Singularities: Limits, Series and Stability

2013

A tree singularity is a surface singularity that consists of smooth components, glued along smooth curves in the pattern of a tree. Such singularities naturally occur as degenerations of certain rational surface singularities. To be more precise, they can be considered as limits of certain series of rational surface singularities with reduced fundamental cycle. We introduce a general class of limits, construct series deformations for them and prove a stability theorem stating that under the condition of finite dimensionality of T 2 the base space of a semi-universal deformation for members high in the series coincides up to smooth factor with the “base space of the limit”. The simplest tree…

A quantum model of Schwarzschild black hole evaporation

1996

We construct a one-loop effective metric describing the evaporation phase of a Schwarzschild black hole in a spherically symmetric null-dust model. This is achieved by quantising the Vaidya solution and by chosing a time dependent quantum state. This state describes a black hole which is initially in thermal equilibrium and then the equilibrium is switched off, so that the black hole starts to evaporate, shrinking to a zero radius in a finite proper time. The naked singularity appears, and the Hawking flux diverges at the end-point. However, a static metric can be imposed in the future of the end-point. Although this end-state metric cannot be determined within our construction, we show tha…

On C1 robust singular transitive sets for three-dimensional flows

1998

Abstract The main goal of this paper is to study robust invariant transitive sets containing singularities for C 1 flows on three-dimensional compact boundaryless manifolds: they are partially hyperbolic with volume expanding central direction. Moreover, they are either attractors or repellers. Robust here means that this property cannot be destroyed by small C 1 -perturbations of the flow.

Rescaling principle for isolated essential singularities of quasiregular mappings

2012

We establish a rescaling theorem for isolated essential singularities of quasiregular mappings. As a consequence we show that the class of closed manifolds receiving a quasiregular mapping from a punctured unit ball with an essential singularity at the origin is exactly the class of closed quasiregularly elliptic manifolds, that is, closed manifolds receiving a non-constant quasiregular mapping from a Euclidean space.

Structural and magnetic properties of the solid solution series Sr2Fe1–xMxReO6(M = Cr, Zn)

2005

Strong correlations between the electronic, structural and magnetic properties have been found during the study of doped double perovskites Sr2Fe1−xMxReO6 (0 ≤ x ≤ 1, M = Zn, Cr). The interplay between the van Hove singularity and the Fermi level plays a crucial role for the magnetic properties. Cr doping of the parent compound Sr2FeReO6 leads to a non-monotonic behaviour of the saturation magnetization and an enhancement for doping levels up to 10%. The Curie temperatures monotonically increase from 401 to 616 K. In contrast, Zn doping leads to a continuous decrease in the saturation magnetization and the Curie temperatures. Superimposed on the electronic effects is the structural influenc…

Valence instabilities and inhomogeneous mixed valence in some ternary europium compounds

1997

Abstract Photoemission spectra and TB-LMTO-ASA band structure calculations of some mixed valency europium compounds hve been studied. The band structures are compared with the band structures of the isostructural lanthanum and strontium compounds. Surprisingly a 4f density of states in the vicinity of the Fermi level is observed in inhomogenous mixed valency EuPd 3 B, Eu 3 S 4 , and EuPdP. Indeed a van Hove Singularity (vHS) derived from the d states of La and Pd or p states of boron or phosphorous are found in La 3 S 4 , LaPd 3 B and SrPdP. The valence instability in the Eu compounds is thus not necessarily due to Eu 4f states. The results also provide some ground for the assumption that i…

Rotation Forms and Local Hamiltonian Monodromy

2017

International audience; The monodromy of torus bundles associated with completely integrable systems can be computed using geometric techniques (constructing homology cycles) or analytic arguments (computing discontinuities of abelian integrals). In this article, we give a general approach to the computation of monodromy that resembles the analytical one, reducing the problem to the computation of residues of polar 1-forms. We apply our technique to three celebrated examples of systems with monodromy (the champagne bottle, the spherical pendulum, the hydrogen atom) and to the case of non-degenerate focus-focus singularities, re-obtaining the classical results. An advantage of this approach …