The monodromy in the Hamiltonian Hopf bifurcation

A simple, straightforward computation is given of the monodromy near an equilibrium point of a Hamiltonian system with two degrees of freedom, which is close to a nondiagonalizable resonance

Selfsimilarity of "Riemann's nondifferentiable function"

This is an expository article about the series f(x) = 1 X n=1 1 n 2 sin(n 2 x); which according to Weierstrass was presented by Riemann as an example of a continuous function without a derivative. An explanation is given of innitely many selfsimilarities of the graph, from which the known results about the dierentiability properties of f(x) are obtained as a consequence

Equivariant cohomology and stationary phase

This is the text of a survey lecture given at the conference on \Symplectic Geometry and its Applications", Keio University, Yokohama, July 21, 1993. I have been stimulated by many people, but I would like to thank especially L. Jerey for her helpful explanations to me of [17]

A characterization of the Ligon-Schaaf regularization map

First, we give an explicit description of all the mappings from the phace space of the Kepler problem to the phase space of the geodesics on the sphere, which transform the constants of motion of the Kepler problem to the angular momentum. Second, among these we describe those mappings which in addition send Kepler solutions to parametrized geodesics. Third, we describe those mappings which in addition are canonical transformations of the respective phase space. Finally we prove that among these the Ligon-Schaaf map is the unique one which maps the collison orbits to the geodesics which pass through the north pole. In this way we also give a new proof that the Ligon-Schaaf map has all the properties described above

Constant terms of powers of a Laurent polynomial

We prove a special case of a conjecture of Mathieu ([Mat]). Conjecture 1 (Mathieu) Let K be a connected real compact Lie group. Let f and g be K-nite functions on K. Assume that for all n 1 the constant term of fn vanishes. Then for all but nitely many n the constant term of fng also vanishes

Statistiek, genetica en epidemiologie : over de zoektocht in ons DNA naar causale varianten

Niet UB, maar tijdelijk ter bevordering van de PDF bestanden in het Leids Repositorium

High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows

We relate high-energy limits of Laplace-type and Dirac-type operators to frame flows on the corresponding manifolds, and show that the ergodicity of frame flows implies quantum ergodicity in an appropriate sense for those operators. Observables for the corresponding quantum systems are matrix-valued pseudodifferential operators and therefore the system remains non-commutative in the high-energy limit. We discuss to what extent the space of stationary high-energy states behaves classically.Comment: 26 pages, latex2

Supersymmetry and localization

We study conditions under which an odd symmetry of the integrand leads to localization of the corresponding integral over a (super)manifold. We also show that in many cases these conditions guarantee exactness of the stationary phase approximation of such integrals.Comment: 16 pages, LATE

Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups

The Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials prod tr{X^{p_1} Omega Y^{q_1} Omega^dagger X^{p_2} ... with the weight exp tr{X Omega Y Omega^dagger} are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries), supplemented by a summation over the Weyl group. This result follows from the study of loop equations in an associated two-matrix integral and may be viewed as the adequate version of Duistermaat-Heckman's theorem for our correlation function integrals. Secondly, the Gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions.Comment: 58 pages; Acknowledgements added; small corrections in appendix A; minor changes & Note Adde