Search results for "singularidades"
showing 4 items of 4 documents
Bifurcations of cuspidal loops
1997
A cuspidal loop for a planar vector field X consists of a homoclinic orbit through a singular point p, at which X has a nilpotent cusp. This is the simplest non-elementary singular cycle (or graphic) in the sense that its singularities are not elementary (i.e. hyperbolic or semihyperbolic). Cuspidal loops appear persistently in three-parameter families of planar vector fields. The bifurcation diagrams of unfoldings of cuspidal loops are studied here under mild genericity hypotheses: the singular point p is of Bogdanov - Takens type and the derivative of the first return map along the orbit is different from 1. An analytic and geometric method based on the blowing up for unfoldings is propos…
Topological invariants of stable immersions of oriented 3-manifolds in R4
2012
Abstract We show that the Z -module of first order local Vassiliev type invariants of stable immersions of oriented 3-manifolds into R 4 is generated by 3 topological invariants: The number of pairs of quadruple points and the positive and negative linking invariants l + and l − introduced by V. Goryunov (1997) [7] . We obtain the expression for the Euler characteristic of the immersed 3-manifold in terms of these invariants. We also prove that the total number of connected components of the triple points curve is a non-local Vassiliev type invariant.
New techniques for classification of multigerms
2018
Abstract The goal of these notes is to give an overview of the state of the art in classification of multigerms. We have tried to make them self-contained but certainly not extensive. The results included here scope most of the research on classification of multigerms carried out in the last 15 years with special emphasis on recent results by the authors of these notes and their collaborators.
Multiple point spaces of finite holomorphic maps
2016
Esta tesis trata sobre espacios múltiples de aplicaciones holomorfas finitas entre variedades complejas. Nuestro enfoque es el de la teoría de singularidades, y las aplicaciones serán consideradas bajo la relación de A-equivalencia, es decir, salvo cambios de coordenadas en partida y llegada. Nos centramos en relacionar propiedades de los espacios de puntos múltiples con propiedades como la A-estabilidad y la A-determinación finita. En generaEl trabajo está organizado de la siguiente manera: El Capítulo 1 contiene los fundamentos básicos necesarios para el resto del trabajo. En el Capítulo 2 definimos los espacios de puntos múltiples de una aplicación. Demostramos que solo hay una manera de…