منابع مشابه
Blow-analytic Equivalence of Two Variable Real Analytic Function Germs
Blow-analytic equivalence is a notion for real analytic function germs, introduced by Tzee-Char Kuo in order to develop the real analytic equisingularity theory. In this paper we give several complete characterisations of blow-analytic equivalence in the two dimensional case in terms of the minimal resolutions, the real tree model for the arrangement of Newton-Puiseux roots, and the cascade blo...
متن کاملMotivic-type Invariants of Blow-analytic Equivalence
To a given analytic function germ f : (R, 0) → (R, 0), we associate zeta functions Zf,+, Zf,− ∈ Z[[T ]], defined analogously to the motivic zeta functions of Denef and Loeser. We show that our zeta functions are rational and that they are invariants of the blow-analytic equivalence in the sense of Kuo. Then we use them together with the Fukui invariant to classify the blow-analytic equivalence ...
متن کاملBlow-analytic Retraction onto the Central Fibre
Let X be a complex analytic space and let f :X → C be a proper complex analytic function with nonsingular generic fibres. By adapting the blowanalytic methods of Kuo we construct a retraction of a neighbourhood of the central fibre f(0) onto f(0). Our retraction is defined by the flow of a real analytic vector field on an oriented real analytic blow-up of X . Then we describe in terms of this b...
متن کاملEquivariant Cohomology and Analytic Descriptions of Ring Isomorphisms
In this paper we consider a class of connected closed G-manifolds with a non-empty finite fixed point set, each M of which is totally non-homologous to zero in MG (or G-equivariantly formal), where G = Z2. With the help of the equivariant index, we give an explicit description of the equivariant cohomology of such a G-manifold in terms of algebra, so that we can obtain analytic descriptions of ...
متن کاملBlow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations
Whether the 3D incompressible Euler and Navier–Stokes equations can develop a finite-time singularity from smooth initial data with finite energy has been one of the most long-standing open questions. We review some recent theoretical and computational studies which show that there is a subtle dynamic depletion of nonlinear vortex stretching due to local geometric regularity of vortex filaments...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2001
ISSN: 0373-0956
DOI: 10.5802/aif.1845