In this work, whose text is in French, the author defines and studies a Reidemeister torsion for hyperbolic three-dimensional manifolds of finite volume. This torsion is an invariant obtained from the combinatorial and the hyperbolic structures of the manifold, and it is studied for closed manifolds and orbifolds, cusped and cone manifolds. The author includes several examples and studies the main properties, involving many aspects of hyperbolic three-manifolds. In particular, it is shown that the torsion of hyperbolic cone manifolds tends to zero for Euclidean degenerations.

This book is intended for graduate students and research mathematicians working in algebraic geometry.

In this book, the authors describe a continuum limit of the Toda ODE system, obtained by taking as initial data for the finite lattice successively finer discretizations of two smooth functions. Using the integrability of the finite Toda lattice, the authors adapt the method introduced by Lax and Levermore for the study of the small dispersion limit of the Korteweg de Vries equations to the case of the Toda lattice. A general class of initial data is considered which permits, in particular, the formation of shocks. A feature of the analysis in this book is an extensive use of techniques from...

The authors employ advances in the theory of operator spaces, also known as quantized functional analysis, to provide a context in which one can compare categories of modules over operator algebras that are not necessarily self-adjoint. Attention is focused on the category of Hilbert modules over an operator algebra and on the category of operator modules over an operator algebra. The module operations are assumed to be completely bounded - usually, completely contractive.

This volume develops a systematic study of time-dependent control processes. The basic problem of null controllability of linear systems is first considered. Using methods of ergodic theory and topological dynamics, general local null controllability criteria are given. Then the subtle question of global null controllability is studied. Next, the random linear feedback and stabilization problem is posed and solved. Using concepts of exponential dichotomy and rotation number for linear Hamiltonian systems, a solution of the Riccati equation is obtained which has extremely good robustness...

This book presents a survey of some recent developments in an important subfield of the new subject of anticipative stochastic analysis. D. Nualart and E. Pardoux have developed into a practicable calculus the theory of stochastic integration of processes not necessarily adapted to the driving Wiener process. This leads to anticipative stochastic differential equations with Skorohod integral and to anticipative Girsanov transformations, both of which are studied in the present work. The anticipative Girsanov transformations constitute the main tool for tackling stochastic differential...

A long open problem in probability theory has been the following: Can the graph of planar Brownian motion be split by a straight line? In this volume, the authors provide a solution, discuss related works, and present a number of open problems.

This memoir provides a detailed study of the effect of non power-like irregularities of (the geometry of) the fractal boundary on the spectrum of fractal drums (and especially of fractal strings). In this work, the authors extend previous results in this area by using the notion of generalized Minkowski content which is defined through some suitable gauge functions other than power functions. (This content is used to measure the irregularity (or fractality) of the boundary of an open set in R ]n by evaluating the volume of its small tubular neighbourhoods). In the situation when the power...

Presents foundational research on two approaches to studying subgroup lattices of finite abelian $p$-groups. This book offers a combinatorial interpretation of the Betti polynomials of the Cohen-Macaulay posets.