Topological classification of linear endomorphisms
The Topology of the solutions of a linear differential equation on Rn
Stable surfaces in euclidean three space : Dedicated to Prof. W. Fenchel in Copenhagen
This paper consists of two related parts. In A we present smooth maps of the real projective plane P with the non euclidean metric ?, into euclidean spaces such that we can read various interesting properties from the image. We mention and indicate some proofs of known facts. This part is expository. In B we consider C?-stable (in the sense of R. Thom) maps of surfaces in E3. We call these "stable surfaces" for short. The Gauss curvature as a measure (? K d?) then exists although the scalar Gauss curvature K may explode at the C?-stable singularities. The infimum of the total absolute curvature (2?)–1 ? |K d?| of a compact surface M equals 4 – ?(M). This infimum can be reached for any surface in the class of stable maps, but not for all surfaces in the class of immersions, as we know. Stable surfaces of minimal total absolute curvature (tight) are given for the exceptions: the projective plane with 0 or 1 handles and the Klein-bottle. Recall that tight (closed) surfaces in EN are also characterized as those that are divided into at most two (connected) parts by any (hyper-)plane.
Topological conjuracy of real projective tranformations
The Topology of holomorphic flows with singularity
A Short history of triangulation and related matters
Conférence donnée au Congress of the Dutch Mathematical Society, Wiskindig Genoorschap, 1778-1978
La Topologie des singularités hyperboliques des actions de R2
Tight embeddings and maps submanifolds of geometrical class three
Differential geometry is a field in which geometry is expressed in analysis, algebra, and calculations, and in which analysis and calculations are sometimes understood in intuitive steps that could be called geometric.
Geometrical class and degree for surfaces in three space
There is no Tight continuous immersion of the Klein bottle into R3
The imbedding radius ?f and the roation number ? of an immersion of a Cech-circle into R2 are used to prove taht there is no tight immersion f of the Klein bottle into R3
Geometry in total absolute curvature theory
This is a (incomplete) report on geometrical results of the last twenty five years in the theory of total absolute curvature, in particular concerning its minimal value in certain classes of embeddings of manifolds.
Hyperbolic manifolds and tesselations : variations on [G.L.T.]
On the Normal Gauss map of a tight smooth surface in R3
On Gradient curves of an analytic function near a critical point
René Thom [T] conjectured that a gradient curve x(t) of an analytic function on Rn, wich descends to the critical point x(?) = 0 ? Rn, called a path, has there a tangent. We prove this in case n = 3 for standard paths and standard functions. For the remaining, rare paths and rare functions we reduce the conjecture for irreductible ? to an evident conjecture and give some arguments in favour of CRT for reductible ?. We did not succeed in elaborating these arguments to a complete proof that covers all cases.
Observables at Infinity and States with Short Range : Correlations in Statistical Mechanics
Abstract : We say that a representation of an algebra of local observables has short-range correlations if any observable which can be measured outside all bounded sets is a multiple of the identity, and that a state has finite range correlations if the corresponding cyclic representation does. We characterize states with short-range correlations by a cluster property. For classical lattice systems and continuous systems with hard cores, we give a definition of equilibrium state for a specific interaction, based on a local version of the grand canonical prescription; an equilibrium state need not be translation invariant. We show that every equilibrium state has a unique decomposition into equilibrium states with short-range correlations. We use the properties of equilibrium states to prove some negative results about the existence of metastable states. We show that the correlation functions for an equilibrium state satisfy the Kirkwood-Salsburg equations; thus, at low activity, there is only one equilibrium state for a given interaction, temperature, and chemical potential. Finally, we argue heuristically that equilibrium states are invariant under time-evolution.
The Classical mechanics of one-dimensional systems of infinitely many particles : I. an Existance theorem
Statistical mechanics of quantum spin systems III
The Classical mechanics of one-dimensional systems of infinitely many particles II : Kinetic theory
A Computer-assisted proof of the Feigenbaum conjectures
A Shorter proof of the existence of the Feigenbaum fixed point
An Introduction to computers and numerical analysis : texte for a series of lectures given at les Houches Session XLIII (Critical phenomena, Random systems, Gauge Theories) August 1984