Titre : | Lectures on spaces of nonpositive curvature | Type de document : | texte imprimé | Auteurs : | Werner BALLMANN, Auteur | Editeur : | Basel : Birkhäuser Verlag | Année de publication : | Cop. 1995 | Collection : | DMV Seminar num. 25 | Importance : | 112 p. | ISBN/ISSN/EAN : | 978-3-7643-5242-4 | Note générale : | With an appendix by Misha Brin : Ergodicity of geodesic flows | Langues : | Anglais (eng) | Mots-clés : | courbure non positive flot géodésique rigidité | Résumé : | Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems, and probability theory.
In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory. With a few exceptions, the book is self-contained and can be used as a text for a seminar or a reading course. Some acquaintance with basic notions and techniques from Riemannian geometry is helpful, in particular for Chapter IV. | Note de contenu : | index, bibliogr. |
Lectures on spaces of nonpositive curvature [texte imprimé] / Werner BALLMANN, Auteur . - Birkhäuser Verlag, Cop. 1995 . - 112 p.. - ( DMV Seminar; 25) . ISBN : 978-3-7643-5242-4 With an appendix by Misha Brin : Ergodicity of geodesic flows Langues : Anglais ( eng) Mots-clés : | courbure non positive flot géodésique rigidité | Résumé : | Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems, and probability theory.
In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory. With a few exceptions, the book is self-contained and can be used as a text for a seminar or a reading course. Some acquaintance with basic notions and techniques from Riemannian geometry is helpful, in particular for Chapter IV. | Note de contenu : | index, bibliogr. |
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