AUTONOMOUS LIMIT OF THE 4-DIMENSIONAL PAINLEV�-TYPE EQUATIONS AND DEGENERATION OF CURVES OF GENUS TWO

We first construct formal foliations on such neighborhoods with holonomy vanishing along many loops, then give the formal / analytic classification of neighborhoods equipped with

In this paper we determine the function /3 in the case of one- dimensional singularities X, taking non-singular arcs, in terms of the Milnor number associated to Xreci- See [La]

10.2. Trivial normal bundle, finite Ueda type: the fundamental isomorphism. Still using the formal classification of [14] as recalled in Section 10.1, one can investigate, without

The proof makes use of the existence of a pair (indeed a pencil) of formal foliations having C as a common leaf, and the fact that neighborhoods are completely determined by

They are entirely devoted to the initial value problem and the long-time behavior of solutions for the two-dimensional incompressible Navier–Stokes equations, in the particular

It will be shown below that the Hamiltonian vector field X f obtained through the symplectic structure on the space of frame-periodic horizontal-Darboux curves leads to

Our main result asserts that it is determined by the base locus of the canonical divisor when the curves degenerate.. Let g: Y ~ T be a proper and smooth morphism with

In section 4, we study the relations between the irreducibility of the difference Galois group of equation (3) and the solutions of an associated Riccati-type equation. We then