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Bifurcation values and stability of algebras of bounded polynomials
-
Krzysztof Kurdyka
,
Maria Michalska
Published/Copyright:
October 8, 2014
Abstract
We show a tight relation between bifurcation values of a fixed polynomial f ∈ R[X; Y] and the family of polynomials bounded on a set { x ∈ R2 | f(x) ≤ c}. If g ∈ R[X; Y] is bounded on {x ∈ R2 | f(x) ≤ c}, then it is bounded on the bigger set {x ∈ R2 | f(x) ≤ c̃} with c < c̃ provided that the interval [c; c̃] does not contain any complex bifurcation value at infinity of f.
Published Online: 2014-10-8
Published in Print: 2014-10-1
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- On the type number of a hypersurface in the 6-dimensional sphere
- On the equality case in Ehrhart’s volume conjecture
- Hamiltonian stability of Hamiltonian minimal Lagrangian submanifolds in pseudo- and para-Kähler manifolds
- The holomorphic symplectic structures on hyper-Kähler manifolds of type A∞
- Bifurcation values and stability of algebras of bounded polynomials
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Articles in the same Issue
- Frontmatter
- On the type number of a hypersurface in the 6-dimensional sphere
- On the equality case in Ehrhart’s volume conjecture
- Hamiltonian stability of Hamiltonian minimal Lagrangian submanifolds in pseudo- and para-Kähler manifolds
- The holomorphic symplectic structures on hyper-Kähler manifolds of type A∞
- Bifurcation values and stability of algebras of bounded polynomials
- Families of bitangent planes of space curves and minimal non-fibration families
- On deformations of G2-structures by Killing vector fields
- Cohomology of 3-points configuration spaces of complex projective spaces
- Slope stability of Fano fourfolds with respect to smooth surfaces
- On quartics with lines of the second kind
