Versal deformation of Hopf surfaces.

1981 ◽  
Vol 1981 (328) ◽  
pp. 22-32 ◽  
Keyword(s):  
Versal Deformation

On the versal deformation of a complex space with an isolated singularity

1972 ◽  
Vol 196 (1) ◽  
pp. 23-29 ◽  
Author(s):  
Arnold Kas ◽  
Michael Schlessinger
Keyword(s):  
Complex Space ◽  
Versal Deformation ◽  
Isolated Singularity

scholarly journals Irreducibility of versal deformation rings in the (p,p)-case for 2-dimensional representations

2015 ◽  
Vol 444 ◽  
pp. 81-123 ◽  
Author(s):  
Gebhard Böckle ◽  
Ann-Kristin Juschka
Keyword(s):  
Versal Deformation ◽  
Deformation Rings

scholarly journals The versal deformation space of a reflexive module on a rational cone

2004 ◽  
Vol 279 (2) ◽  
pp. 613-637 ◽  
Author(s):  
Trond Stølen Gustavsen ◽  
Runar Ile
Keyword(s):  
Versal Deformation ◽  
Deformation Space ◽  
Reflexive Module

Image Milnor number and 𝒜e-codimension for maps between weighted homogeneous irreducible curves

2020 ◽  
Vol 20 (3) ◽  
pp. 319-330
Author(s):  
D. A. H. Ament ◽  
J. J. Nuño-Ballesteros ◽  
J. N. Tomazella
Keyword(s):  
Milnor Number ◽  
Versal Deformation ◽  
Minimum Number ◽  
Vanishing Cycles ◽  
One To One

AbstractLet (X, 0) ⊂ (ℂn, 0) be an irreducible weighted homogeneous singularity curve and let f : (X, 0) → (ℂ2, 0) be a finite map germ, one-to-one and weighted homogeneous with the same weights of (X, 0). We show that 𝒜e-codim(X, f) = μI(f), where the 𝒜e-codimension 𝒜e-codim(X, f) is the minimum number of parameters in a versal deformation and μI(f) is the image Milnor number, i.e. the number of vanishing cycles in the image of a stabilization of f.

ANALYSIS OF THE TAKENS–BOGDANOV BIFURCATION ON m-PARAMETERIZED VECTOR FIELDS

2010 ◽  
Vol 20 (04) ◽  
pp. 995-1005 ◽  
Author(s):  
FRANCISCO A. CARRILLO ◽  
FERNANDO VERDUZCO ◽  
JOAQUÍN DELGADO
Keyword(s):  
Imaginary Axis ◽  
Vector Fields ◽  
Center Manifold ◽  
Sufficient Conditions ◽  
Versal Deformation ◽  
Two Dimensional ◽  
Double Zero ◽  
Zero Eigenvalue ◽  
The Family ◽  
Parameterized Family

Given an m-parameterized family of n-dimensional vector fields, such that: (i) for some value of the parameters, the family has an equilibrium point, (ii) its linearization has a double zero eigenvalue and no other eigenvalue on the imaginary axis, sufficient conditions on the vector field are given such that the dynamics on the two-dimensional center manifold is locally topologically equivalent to the versal deformation of the planar Takens–Bogdanov bifurcation.

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