Geometry of continued fractions
Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical th...
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2013. |
| Collection: | Algorithms and Computation in Mathematics
26 |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Geometry of continued fractions, Oleg Karpenkov, Berlin, Springer, 2013, 1 vol. (XVII-405 p.), Algorithms and computation in mathematics, 978-3-642-39367-9, Texte imprimé |
Table des matières:
- Preface Introduction Part 1. Regular continued fractions: Chapter 1. Classical notions and definitions Chapter 2. On integer geometry Chapter 3. Geometry of regular continued fractions Chapter 4. Complete invariant of integer angles Chapter 5. Integer trigonometry for integer angles Chapter 6. Integer angles of integer triangles Chapter 7. Continued fractions and SL(2; Z) conjugacy classes. Elements of Gauss Reduction Theory. Markoff spectrum Chapter 8. Lagrange theorem Chapter 9. Gauss-Kuzmin statistics Chapter 10. Geometric approximation aspects Chapter 11. Geometry of continued fractions with real elements and the second Kepler law Chapter 12. Integer angles of polygons and global relations to toric singularities Part 2. Klein polyhedra: Chapter 13. Basic notions and definitions of multidimensional integer geometry Chapter 14. On empty simplices, pyramids, parallelepipeds Chapter 15. Multidimensional continued fractions in the sense of Klein Chapter 16. Dirichlet groups and lattice reduction Chapter 17. Periodicity of Klein polyhedra. Generalization of Lagrange theorem Chapter 18. Multidimensional Gauss-Kuzmin statistics Chapter 19. On construction of multidimensional continued fractions Chapter 20. Gauss Reduction in higher dimensions Chapter 21. Decomposable forms. Relation to Littlewood and Oppenheim conjectures Chapter 22. Approximation of maximal commutative subgroups Chapter 23. Other generalizations of continued fractions Bibliography