Related papers: Sur le th\'eor\`eme KAM

We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.

In this paper, we strengthen the splitting theorem proved in [14, 15] and provide a different approach using ideas from the weak KAM theory.

We introduce S-nondegenerate formal CR maps and establish their convergence (revision of a preliminary version).

In this note we show how improved theoretical analysis combined with recent experimental data coming from NA48/2 concerning $K^+ \to \pi^+ \pi^0 \gamma$ decay shed light on the dynamics of the $s \rightarrow d \gamma$ transition.…

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

This note is a comment on the "quantum interferometry" section of Reference [1]. It points out that the methods of that section can be applied to more general states than the ones that are discussed in Ref. [1].

The present status of CP violation in decays of neutral kaons is reviewed. In addition selected rare decays of both K and B mesons are discussed. The emphasis is in particular on observables that can be reliably calculated and thus offer…

In the theory of antiferromagnetism, the staggered field---an external magnetic field that alternates in sign on atomic length scales---is used to select the classical N\'eel state from a quantum magnet, but justification is missing. This…

A new method to extract the weak phase $\gamma$ is suggested by exploiting B ---> D K^{(*)} decay modes that are not Cabibbo suppressed, using the isospin relations, and ignoring the annihilation diagram as usual. Assuming $3 \times 10^8…

I review recent developments in rare and radiative kaon decays from the theory side, with emphasis on those modes that are actively analyzed by the experimental collaborations.

Masking of data is a method to protect information by shielding it from a third party, however keeping it usable for further usages like application development, building program extensions to name a few. Whereas it is possible for…

In this paper, we establish an abstract infinite dimensional KAM theorem dealing with normal frequencies in weaker spectral asymptotics \Omega_{i}(\xi)=i^d+o(i^{d})+o(i^{\delta}), where $d>0, \delta<0$, which can be applied to a large class…

In this note we prove that, under a weak condition, small deformations of a compact balanced manifold are also balanced. This condition is satisfied on the twistor space over a compact self-dual four manifold.

The purpose of this note is to clarify the conditions under which the first-order generalize-harmonic representation of the vacuum Einstein evolution system is linearly degenerate.

In this note we use the normal forms of the completely resonant non--linear Schr\"odinger equation on a torus (NLS) derived in previous work in order to produce, under a KAM algorithm, large families of stable and unstable quasi periodic…

Degeneracy of the eigenvalues of the Pauli-Fierz Hamiltonian with spin 1/2 is proven by the Kramers degeneracy theorem. The Pauli-Fierz Hamiltonian at fixed total momentum is also investigated.

It is known after the works of Mahler, Kleinbock, Margulis, Sprind\v{z}uk and others that very well approximated numbers on a manifold form a zero measure set, assuming non-degeneracy conditions. These non-degeneracy conditions are, in many…

In this article we study compact K\ahler manifolds satisfying a certain nonnegativity condition on the bisectional curvature. Under this condition, we show that the scalar curvature is nonnegative and that the first Chern class is positive…

It has long been recognized that emission of radiation from atoms is not an intrinsic property of individual atoms themselves, but it is largely affected by the characteristics of the photonic environment and by the collective interaction…

Based on quantitative ``{\sc kam} theory'', we state and prove two theorems about the continuation of maximal and whiskered quasi--periodic motions to slightly perturbed systems exhibiting proper degeneracy. Next, we apply such results to…