Fixed points and entropy for non solvable dynamics onC, O

This work generalizes for any non-solvable pseudo-groups of Diff_0,C the existence of fixed points arbitrarly close to the origin already proved in the generic case [G-M,Wil]. An elementary proof of the Sherbakov-Nakai's density theorem [Na] is added with moreover some more precision about the derivative of a germ sending a point close to an other one. At last the topological entropy and the entropy of fixed points are strictly positive for such pseudo-groups as in [Wi] and [G-M, Wi2].Dedicated to the memory of R. MañéSupported by CNRS-Dijon and CNPq-IMPA, PICS. n^o. 177.     

C-半群与C_0—半群的关系

在这篇文章中证明了C-半群在限制空间中为C_0-半群,首次讨论了C-半群的解析性     

On the order of the automorphism group of foliations

Let be a holomorphic foliation with ample canonical bundle on a smooth projective surface X. We obtain an upper bound on the order of its automorphism group which depends only on and provided this group is finite. Here, and are the canonical bundles of and X, respectively.     

Schwarz引理与Schwarz-Pick引理在单位球B_n上的推广

对单复变中的Schwarz引理与Schwarz-Pick引理在C~n中的超球上进行了推广.考虑C~n中单位球B_n上模小于1的全纯函数f(z),并在f(0)=0的条件下给出函数在原点的任意阶导数的估计.更进一步地,得到了B_n上模小于1的任意全纯函数在任意点的高阶导数的估计.     

The number of periodic solutions of some analytic equations of Abel type

New results are proved to estimate the number of periodic solutions of a differential equation of Abel type by using a modification of a technique introduced by Ilyashenko. The main tool is an estimate on the number of zeros of a holomorphic function. A concrete example is analyzed but the results are presented to make the method flexible and applicable to other equations.     

A correspondence for isometric immersions into product spaces and its applications

We present a correspondence for isometric immersions that are graphs in Riemannian or semi-Riemannian warped product spaces. We use this correspondence to give several existence and non-existence theorems for hypersurfaces in Riemannian or Lorentzian spaces. In the case of surfaces, we obtain further applications regarding height estimates, harmonic representation of surfaces and the existence of holomorphic quadratic differentials in homogeneous and non-homogeneous spaces.     

Virial inversion and density functionals

We prove a novel inversion theorem for functionals given as power series in infinite-dimensional spaces. This provides a rigorous framework to prove convergence of density functionals for inhomogeneous systems with applications in classical density function theory, liquid crystals, molecules with various shapes or other internal degrees of freedom. The key technical tool is the representation of the inverse via a fixed point equation and a combinatorial identity for trees, which allows us to obtain convergence estimates in situations where Banach inversion fails.