asymptotic completeness for n body stark hamiltonians we prove asymptotic completeness for short and long rangen body stark hamiltonians with local singularities of at most coulomb type our results include the usual models for atoms and molecules

nonmonotonic twist maps abstract we investigate a family of nonmonotonic radial twist maps constructed by unfolding the linear twist function we find several new modes of reconnection and derive conditions for them to occur reconnection and bifurcation of higher order resonances are studied in detail including vortex pairs and triplets the structural instability of some of these exotic figures is mitigated by the presence of chaotic separatrix layers invariant curves of involution pairs are utilized to locate and chart their often very complex metamorphoses

asymptotic completeness for long range many particle systems with stark effect ii we prove the existence and the asymptotic completeness of the dollard type modified wave operators for many particle stark hamiltonians with long range potentials

complete poincare sections and tangent sets trying to extend a local definition of a surface of a section and the corresponding poincare map to a global one one can encounter severe difficulties we show that global transverse sections often do not exist for hamiltonian systems with two degrees of freedom as a consequence we present a method to generate the so called w section which by construction will be intersected by almost all orbits depending on the type of tangent set in the surface of the section we distinguish five types of w sections the method is illustrated by a number of examples most notably the quartic potential and the double pendulum w sections can also be applied to higher dimensional hamiltonian systems and to dissipative systems

absence of singular continuous spectrum for certain self adjoint operators we give a sufficient condition for a self adjoint operator to have the following properties in a neighborhood of a pointe of its spectrum a its point spectrum is finite b its singular continuous spectrum is empty c its resolvent satisfies a class of a priori estimates

the vanishing twist in the restricted three body problem abstract this paper demonstrates the existence of twistless tori and the associated reconnection bifurcations and meandering curves in the planar circular restricted three body problem near the lagrangian equilibrium l 4 a twistless torus is created near the tripling bifurcation of the short period family decreasing the mass ratio leads to twistless bifurcations which are particularly prominent for rotation numbers 3 10 and 2 7 this scenario is studied by numerically integrating the regularised hamiltonian flow and finding rotation numbers of invariant curves in a two dimensional poincare map to corroborate the numerical results the birkhoff normal form at l 4 is calculated to eighth order truncating at this order gives an integrable system and the rotation numbers obtained from the birkhoff normal form agree well with the numerical results a global overview for the mass ratio 4 3 is presented by showing lines of constant energy and constant rotation number in action space

a method for accurate computation of the rotation and the twist numbers of invariant circles a method is proposed for accurate evaluation of the rotation and the twist numbers of invariant circles in two degrees of freedom hamiltonian systems or two dimensional symplectic maps the method uses the recurrence of orbits to overcome the problems usually arising because of the multivalued character of the angles due to modulo 2 pi that have to be added in order to evaluate the above numbers furthermore best convergent demoninators q n of these numbers can be estimated and we show that under a proper treatment of the sequences of q n iterations the accuracy is of the order of 1 q n 4 c 2001 elsevier science b v all rights reserved

the stability of the lagrange triangular point and a theorem of arnold deprit and deprit bartholome 5 computed the normal form for the hamiltonian of the planar restricted three body problem at the lagrange equilateral triangle equilibrium point up to terms of order 4 this normalization was carried out for all mass ratios p smaller than routh s critical mass ratio p1 i 1 j 9 except for two values p2 and pi at p2 and u the ratio of the linearized frequencies is 1 2 and 1 3 respectively and so low order resonance terms appear this normalization was carried out in order to apply the kam theory to prove the stability of this equilibrium point from the coefficients of the normal form they computed a quantity d defined below which when non zero establishes the stability of the equilibrium point they found that d 0 for 0 cp p u p2 p and p the value u does not correspond to resonance but is simply a point where the quantity d4 changes sign in this paper we shall establish the full stability of the lagrange equilibrium point in the planar restricted three body problem even in the case when u p we do this by computing by machine the normal form up to terms of order 6 and then applying a theorem of arnold 3 which establishes the stability of the equilibrium even in degenerate cases russman lo announced a theorem which implies that the equilibrium is isoenergetic stable when p p by isoenergetic stable he means that the system is stabie only on the energy surface defined by the energy at the equilibrium itself unfortunately there is not even an indication of the proof arnold announced his theorem in a doklady note with only a sketch of a proof the sketch indicates that his proof requires completely redoing all

another look at the saddle centre bifurcation vanishing twist abstract in the saddle centre bifurcation a pair of periodic orbits is created out of nothing in a hamiltonian system with two degrees of freedom it is the generic bifurcation with multiplier one we show that out of nothing should be replaced by out of a twistless torus more precisely we show that invariant tori of the normal form have vanishing twist right before the appearance of the new orbits vanishing twist means that the derivative of the rotation number with respect to the action for constant energy vanishes we explicitly derive the position of the twistless torus in phase and in parameter space near the saddle centre bifurcation the theory is applied to the area preserving henon map

asymptotic completeness for n body short range quantum systems a new proof we give an alternative geometrical proof of asymptotic completeness for an arbitrary number of quantum particles interacting through shortrange pair potentials it relies on an estimate showing that the intercluster motion concentrates asymptotically on classical trajectories

propagation estimates for n body schroedinger operators we prove propagation estimates of strong type for long rangen body hamiltonians emphasis is on phase space analysis in the free channel region

the n particle scattering problem asymptotic completeness for short range systems on demontre la completude asymptotique pour des systemes de mecanique quantique a courte portee constitues d un nombre arbitraire de particules

spectral theory of time periodic many body systems we study the spectrum of the monodromy operator for an n body quantum system in a time periodic external field with time mean equal to zero this includes ac stark and circularly polarized fields and pair potentials with a local singularity up to and including the coulomb singularity in the framework of floquet theory we prove a local commutator estimate and use it to prove a limiting absorption principle for the floquet hamiltonian as well as exponential decay estimates on non threshold eigenfunctions these two results are then used to obtain a second order perturbation theory for embedded eigenvalues the principal tool is a new extended mourre theory

on the numerical computation of poincare maps abstract this note describes a method for finding simply and accurately the intersections of a numerically integrated trajectory with a surface of section

asymptotic completeness for n body quantum systems with long range interactions in a time periodic electric field we show the asymptotic completeness for n body quantum systems with long range interactions in a time periodic electric field whose mean in time is non zero where n 2 one of the main ingredients of this paper is to give some propagation estimates for physical propagators generated by time periodic hamiltonians which govern the systems under consideration

asymptotic completeness of long range n body quantum systems where x is a euclidean space and lra a e a is a finite family of projections onto certain subspaces xa of x we will always assume that the family xa a e a is closed with respect to the algebraic sum and contains xamin 0 the class of operators of the form 0 2 is a generalization of 0 1 up to a linear change of coordinates in the configuration space x they usually go under the name of generalized n body schrbdinger operators and were first considered in a in what follows we will drop the word generalized we refer the reader to rsi vol iii for a general introduction to n body schr6dinger operators defined as in equation 0 1 we will consistently use the definition 0 2 and assume that the reader is familiar with the physical meaning of various objects under study

existence of solutions for schrodinger evolution equations we study the existence uniqueness and regularity of the solution of the initial value problem for the time dependent schrodinger equationi u t 1 2 u v t x u u 0 u0 we provide sufficient conditions onv t x such that the equation generates a unique unitary propagatoru t s and such thatu t s u0ec1 l2 c0 h2 n foru0eh2 n the conditions are general enough to accommodate moving singularities of type x 2 n 4 or x n 2 n 3

spectral analysis of n body stark hamiltonians we prove that the spectrum for a large class ofn body stark hamiltonians is purely absolutely continuous we need slow decay at infinity and local singularities of at most coulomb type in particular our results include the usual models for atoms and molecules

quasisymmetric models for the analysis of square contingency tables summary a parametric model is presented for the analysis of square contingency tables where there is a one to one correspondence between the categories of the row variable and the categories of the column variable the model is applicable to cross classifications where the categories are unordered partially ordered or completely ordered but the interpretation of the model and associated parameters is most straightforward when the categories are at least partially ordered connections with the mover stayer model and the usual model of quasisymmetry are described two data sets are used to illustrate the utility of the model