On the cohomology of the complement of the bifurcation diagram of the singularity \(A_ \mu\)
type: Item
instance of: scholarly article
title: On the cohomology of the complement of the bifurcation diagram of the singularity \(A_ \mu\)
zbMATH Open document ID: 0811.58016
publication date: 1994-12-05T00:00:00Z
review text: Let \(\mathbb{C}^{\mu - 1}\) be the space of polynomials \(f(z) = z^{\mu - 1} + a_ 1 z^{\mu - 1} + \dots + a_{\mu- 1} z\), \(a_ i \in \mathbb{C}\). The space of polynomials of general position in \(\mathbb{C}^{\mu - 1}\) is the complement to a hypersurface \(\Xi\) consisting of two irreducible components. One of them is caustic \(\Sigma\) formed by the polynomials with degenerate critical points \((f'(z) = f''(z) = 0)\). The other -- Maxwell stratum \(M\) -- is the closure of the set of polynomials with coinciding critical values. The set \(\Xi\) is the function bifurcation diagram of the singularity \(A_ \mu\). In the article under review the local cohomology ring of the complement of the bifurcation diagram is studied.
Mathematics Subject Classification ID: 58E07
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
zbMATH DE Number: 687599
zbMATH Keywords: bifurcation diagram
zbMATH Keywords: singularity
zbMATH Keywords: local cohomology ring
author: Nikita Nekrasov
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
cites work: Small denominators. I. Mappings of the circumference onto itself
cites work: Pseudocharacters on the group \(\text{SL}(2,\mathbb{Z})\)
cites work: Q5727753
cites work: Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
cites work: Scaling of the Arnold tongues
cites work: Rotation Sets of Toral Flows
cites work: Resonance regions for Mathieu type dynamical systems on a torus
cites work: Attractors on an N-torus: Quasiperiodicity versus chaos
cites work: Resonance Zones in Two-Parameter Families of Circle Homeomorphisms
cites work: Resonance regions for families of torus maps
cites work: Rotation Sets for Maps of Tori
cites work: Bifurcations and stability of families of diffeomorphisms
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 687599