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Hamiltonian stability and subanalytic geometry

Laurent Niederman (2006)

Annales de l’institut Fourier

In the 70’s, Nekhorochev proved that for an analytic nearly integrable Hamiltonian system, the action variables of the unperturbed Hamiltonian remain nearly constant over an exponentially long time with respect to the size of the perturbation, provided that the unperturbed Hamiltonian satisfies some generic transversality condition known as steepness. Using theorems of real subanalytic geometry, we derive a geometric criterion for steepness: a numerical function h which is real analytic around a...

Hermitian (a,b)-modules and Saito's "higher residue pairings"

Piotr P. Karwasz (2013)

Annales Polonici Mathematici

Following the work of Daniel Barlet [Pitman Res. Notes Math. Ser. 366 (1997), 19-59] and Ridha Belgrade [J. Algebra 245 (2001), 193-224], the aim of this article is to study the existence of (a,b)-hermitian forms on regular (a,b)-modules. We show that every regular (a,b)-module E with a non-degenerate bilinear form can be written in a unique way as a direct sum of (a,b)-modules E i that admit either an (a,b)-hermitian or an (a,b)-anti-hermitian form or both; all three cases are possible, and we give...

Holomorphic bijections of algebraic sets

Sławomir Cynk, Kamil Rusek (1997)

Annales Polonici Mathematici

We prove that every holomorphic bijection of a quasi-projective algebraic set onto itself is a biholomorphism. This solves the problem posed in [CR].

Invariants of bi-Lipschitz equivalence of real analytic functions

Jean-Pierre Henry, Adam Parusiński (2004)

Banach Center Publications

We construct an invariant of the bi-Lipschitz equivalence of analytic function germs (ℝⁿ,0) → (ℝ,0) that varies continuously in many analytic families. This shows that the bi-Lipschitz equivalence of analytic function germs admits continuous moduli. For a germ f the invariant is given in terms of the leading coefficients of the asymptotic expansions of f along the sets where the size of |x| |grad f(x)| is comparable to the size of |f(x)|.

Invariants of equidimensional maps

Joachim H. Rieger (2003)

Banach Center Publications

To a given complex-analytic equidimensional corank-1 germ f, one can associate a set of integer 𝓐-invariants such that f is 𝓐-finite if and only if all these invariants are finite. An analogous result holds for corank-1 germs for which the source dimension is smaller than the target dimension.

Killing divisor classes by algebraisation

Alexandru Buium (1985)

Annales de l'institut Fourier

It is proved that any isolated singularity of complete intersection has an algebraisation whose divisor class group is finitely generated.

Currently displaying 61 – 80 of 195