인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

This article was widely circulated as a preprint, about 12 years ago. At that time the Bulletin did not accept research announcements, and after a couple of attempts to publish it, I gave up, and the preprint did not find a home. I very soon saw that there were many ramifications of this theory, and I talked extensively about it in a number of places. One year I devoted my graduate course to this theory, and notes of Bill Floyd and Michael Handel from that course were circulated for a while. The participants in a seminar at Orsay in 1976-1977 went over this material, and wrote a volume [FLP] including some original material as well. Another good general reference, from a somewhat different point of view, is a set of notes of lectures by A. Casson, taken by S. Bleiler [CasBlei]. There are by now several alternative ways to develop the classification of diffeomorphisms of surfaces described here. At the time I originally discovered the classification of diffeomorphism of surfaces, I was unfamiliar with two bodies of mathematics which were quite relevant: first, Riemann surfaces, quasiconformal maps and Teichmiiller's theory; and second, Nielsen's theory of the dynamical behavior of surface at infinity, and his near-understanding of geodesic laminations. After hearing about the classification of surface automorphisms from the point of view of the space of measured foliations, Lipman Bers [Bersl] developed a proof of the classification of surface automorphisms from the point of view of Teichmüller theory, generalizing Teichmiiller's theorem by allowing the Riemann surface to vary as well as the map. Dennis Sullivan first told me of some neglected articles by Nielsen which might be relevant. This point of view has been discussed by R. Miller, J. Gilman, M. Handel and me. The analogous theory, of measured laminations and 2-dimensional train tracks in three dimensions, has been considerable development. This has been applied to reinterpret some of Haken's work, to classify incompressible surfaces in particular classes of 3-manifolds in papers by me, Hatcher, Floyd, Oertel and others in various combinations. Shalen, Morgan, Culler and others have developed the related theory of groups acting on trees, and its relation to measured laminations, to define and analyze compactifications of representation spaces of groups in SL(2, C) and SO(n, 1); this has many interesting applications, including the theory of incompressible surfaces in 3-manifolds.

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On the geometry and dynamics of diffeomorphisms of surfaces

Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S to G(R), construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hyperbolic; the moduli space of positive representations is a topologically trivial open domain in the space of all representations. When S have holes, we defined two moduli spaces closely related to the moduli spaces of G-local systems on S. We show that they carry a lot of interesting structures. In particular we define a distinguished collection of coordinate systems, equivariant under the action of the mapping class group of S. We prove that their transition functions are subtraction free. Thus we have positive structures on these moduli spaces. Therefore we can take their points with values in any positive semifield. Their positive real points provide the two higher Teichmuller spaces related to G and S, while the points with values in the tropical semifields provide the lamination spaces. We define the motivic avatar of the Weil–Petersson form for one of these spaces. It is related to the motivic dilogarithm.

/pdf/moduli-spaces-of-local-systems-and-higher-teichmuller-theory-36h32nsutb.pdf

Moduli spaces of local systems and higher Teichmüller theory

In this chapter we will embark upon the task of systematically identifying important specific phenomena associated with the asymptotic behavior of smooth dynamical systems We will build upon the results of our survey of specific examples in Chapter 1 as well as on the insights gained from the general structural approach outlined and illustrated in Chapter 2 Most of the properties discussed in the present chapter are in fact topological invariants and can be defined for broad classes of topological dynamical systems, including symbolic ones The predominance of topological invariants fits well with the picture that emerges from the considerations of Sections 21, 23, 24, and 26 The considerations of the previous chapter make it very plausible that smooth dynamical systems are virtually never differentiably stable and can only rarely be classified locally up to smooth conjugacy In contrast, structural and the related topological stability seem to be fairly widespread phenomena We will consider three broad classes of asymptotic invariants: (i) growth of the numbers of orbits of various kinds and of the complexity of orbit families, (ii) types of recurrence, and (iii) asymptotic distribution and statistical behavior of orbits The first two classes are of a purely topological nature; they are discussed in the present chapter The last class is naturally related to ergodic theory and hence we will provide an introduction to key aspects of that subject This will require some space so we put that material into a separate chapter The two chapters are intimately connected

Introduction to the Modern Theory of Dynamical Systems: PRINCIPAL CLASSES OF ASYMPTOTIC TOPOLOGICAL INVARIANTS

A framework is developed in which new connections to a growing network optimize geometric trade-offs between popularity and similarity, instead of simply preferring popular nodes; this approach accurately describes the large-scale evolution of various networks. Preferential attachment is a mechanism that attempts to explain the emergence of scaling in growing networks. If new connections are preferentially established with more popular nodes in a network, then the network is scale-free. So, because 'popularity is attractive', does preferential attachment predict network evolution? This study shows that popularity is a strong force in shaping complex network structure and dynamics, but so too is similarity. The authors develop a model that increases the accuracy of network-evolution predictions by considering the trade-offs between popularity and similarity. The model accurately describes large-scale evolution of technological (Internet), social and metabolic networks, predicting the probability of new links with high precision. The principle1 that ‘popularity is attractive’ underlies preferential attachment2, which is a common explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting distribution of the number of connections possessed by nodes follows power laws3,4, as observed in many real networks5,6. Preferential attachment has been directly validated for some real networks (including the Internet7,8), and can be a consequence of different underlying processes based on node fitness, ranking, optimization, random walks or duplication9,10,11,12,13,14,15,16. Here we show that popularity is just one dimension of attractiveness; another dimension is similarity17,18,19,20,21,22,23,24. We develop a framework in which new connections optimize certain trade-offs between popularity and similarity, instead of simply preferring popular nodes. The framework has a geometric interpretation in which popularity preference emerges from local optimization. As opposed to preferential attachment, our optimization framework accurately describes the large-scale evolution of technological (the Internet), social (trust relationships between people) and biological (Escherichia coli metabolic) networks, predicting the probability of new links with high precision. The framework that we have developed can thus be used for predicting new links in evolving networks, and provides a different perspective on preferential attachment as an emergent phenomenon.

Popularity versus similarity in growing networks

Bouts des variétiés hyperboliques de dimension 3

The geometry of Teichmüller space via geodesic currents.

L'article presente un systeme de coordonnees locales holomorphes pour l'espace des varietes hyperboliques de dimension 3 qui ont le groupe fondamental d'une surface. Ces coordonnees dependent du choix d'une lamination geodesique sur la surface, et forment une complexification des coordonnees de decalage introduites par Thurston pour l'espace de Teichmuller. La partie imaginaire de ces coordonnees mesure la courbure d'une surface plissee realisant la lamination geodesique. De plus, nous montrons comment ces coordonnees sont reliees, par l'intermediaire de la forme symplectique de Thurston sur l'espace des laminations geodesiques mesurees, a la fonction longueur complexe et a sa differentielle.

/pdf/shearing-hyperbolic-surfaces-bending-pleated-surfaces-and-4bh105l9or.pdf

Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form

© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1983, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www. elsevier.com/locate/ansens) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

/pdf/scindements-de-heegaard-des-espaces-lenticulaires-2bhyrn32v1.pdf

Scindements de Heegaard des espaces lenticulaires

/pdf/cobordism-of-automorphisms-of-surfaces-4ys2wi2rw4.pdf

Francis Bonahon

Papers

Bouts des variétiés hyperboliques de dimension 3

The geometry of Teichmüller space via geodesic currents.

Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form

Scindements de Heegaard des espaces lenticulaires

Cobordism of automorphisms of surfaces