The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the postNewtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail eects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

/pdf/gravitational-radiation-from-post-newtonian-sources-and-g96j1cyq78.pdf

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

/pdf/differential-equations-and-dynamical-systems-3chsjx2k45.pdf

Differential Equations and Dynamical Systems

/pdf/introduction-to-the-modern-theory-of-dynamical-systems-1eced70mum.pdf

Introduction to the Modern Theory of Dynamical Systems

A group theoretical approach to hydrodynamics considers hydrodynamics to be the differential geometry of diffeomorphism groups. The principle of least action implies that the motion of a fluid is described by the geodesics on the group in the right-invariant Riemannian metric given by the kinetic energy. Investigation of the geometry and structure of such groups turns out to be useful for describing the global behavior of fluids for large time intervals.

Topological methods in hydrodynamics

We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software.

/pdf/the-quadratic-eigenvalue-problem-4ozf2mxadi.pdf

The Quadratic Eigenvalue Problem

Introduction to Ordinary Differential Equations * Linear Systems and Stability of Nonlinear Systems * Applications * Hyperbolic Theory * Continuation of Periodic Solutions * Homoclinic Orbits, Melnikov?s Method, and Chaos * Averaging * Local Bifurcation * References * Index.

http://www.math.ecnu.edu.cn/~zmwang/teaching/Advanced_ODE-2014-2015/1-Textbook_and_Reference_book/2-Ordinary%20Differential%20Equations%20with%20Applications.pdf

Ordinary Differential Equations with Applications

Introduction Semigroups on Banach spaces and evolution semigroups Evolution families and Howland semigroups Characterizations of dichotomy for evolution families Two applications of evolution semigroups Linear skew-product flows and Mather evolution semigroups Characterizations of dichotomy for linear skew-product flows Evolution operators and exact Lyapunov exponents Bibliography List of notations Index.

/pdf/evolution-semigroups-in-dynamical-systems-and-differential-3jgpsw9flj.pdf

Evolution Semigroups in Dynamical Systems and Differential Equations

On etudie un probleme de bifurcation dans des familles de champs de vecteurs analytiques plans qui ont un centre non degenere a l'origine pour toutes les valeurs d'un parametre λ∈R N . On definit la fonction periode: (ξ,λ)→P(ξ,λ). On determine les points critiques de cette fonction pres du centre avec λ comme parametre de bifurcation

/pdf/bifurcation-of-critical-periods-for-plane-vector-fields-2dvziqyxfr.pdf

Carmen Chicone

Papers

Ordinary Differential Equations with Applications

Evolution Semigroups in Dynamical Systems and Differential Equations

Bifurcation of critical periods for plane vector fields

The monotonicity of the period function for planar Hamiltonian vector fields

Bifurcation of limit cycles from quadratic isochrones