Related papers: Comments about Hilbert's 16'th problem

We study the linearization problem of germs of holomorphic diffeomorphisms with resonant linear part. The formal linearization requires in general an infinite number of algebraic relations to be satisfied by the coefficients of the power…

We introduce a new family of thermostat flows on the unit tangent bundle of an oriented Riemannian $2$-manifold. Suitably reparametrised, these flows include the geodesic flow of metrics of negative Gauss curvature and the geodesic flow…

The notion of type of a differential 2-form in four variables is introduced and for 2-forms of type < 4, local normal models are given. If the type of a 2-form $\Omega$ is 4, then the equivalence under diffeomorphisms of $\Omega$ is reduced…

We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of completely integrable Hamiltonian systems are investigated.…

We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution…

We study the Laplacian flow of a $\mathrm{G}_2$-structure where this latter structure is claimed to be Locally Conformal Parallel. The first examples of long time solutions of this flow with the Locally Conformal Parallel condition are…

Following Hausel-Hitchin, we investigate core Lagrangians and upward flows in Hilbert schemes of points on elliptic surfaces. We compute the scheme-theoretic multiplicities of core Lagrangians, as well as the equivariant multiplicities of…

In this article, we introduce equivariant formal deformation theory of associative algebra morphisms. We introduce an equivariant deformation cohomology of associative algebra morphisms and using this we study the equivariant formal…

This paper generalizes Bismut's equivariant Chern character to the setting of abelian gerbes. In particular, associated to an abelian gerbe with connection, an equivariantly closed differential form is constructed on the space of maps of a…

In this article we propose a new and so-called holomorphic deformation scheme for locally convex algebras and Hopf algebras. Essentially we regard converging power series expansion of a deformed product on a locally convex algebra, thus…

T. Mostowski showed that every (real or complex) germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that every (real or complex) analytic function germ, defined on a possibly singular analytic…

We consider a wide class of fully nonlinear integro-differential equations that degenerate when the gradient of the solution vanishes. By using compactness and perturbation arguments, we give a complete characterization of the regularity of…

Any deformation of a Weyl or Clifford algebra can be realized through some change of generators in the undeformed algebra. Here we briefly describe and motivate our systematic procedure for constructing all such changes of generators for…

We solve Hilbert's fifth problem for local groups: every locally euclidean local group is locally isomorphic to a Lie group. Jacoby claimed a proof of this in 1957, but this proof is seriously flawed. We use methods from nonstandard…

We consider the 1-harmonic flow of maps from a bounded domain into a submanifold of a Euclidean space, i.e. the gradient flow of the total variation functional restricted to maps taking values in the manifold. We restrict ourselves to…

This paper presents new results in the theory of number theoretic Hilbert (NHT) transforms. New polymorphic solutions have been found for the 14-point and 16-point transforms. Several transform pairs are computed and solutions found for…

The local generality of the space of solitons for the Laplacian flow of closed $G_2$-structures is analyzed, and it is shown that the germs of such structures depend, up to diffeomorphism, on 16 functions of 6 variables (in the sense of E.…

Deformation theory is treated for locally notherian formal schemes (non necessarily smooth). The cotangent complex is defined in the derived category through the homology localization functor. The basic properties and results of a…

We study analytic integrable deformations of the germ of a holomorphic foliation given by $df=0$ at the origin $0 \in \mathbb C^n, n \geq 3$. We consider the case where $f$ is a germ of an irreducible and reduced holomorphic function. Our…

A new approach to the analytic theory of difference equations with rational and elliptic coefficients is proposed. It is based on the construction of canonical meromorphic solutions which are analytical along "thick paths". The concept of…