Arithmetic on a punctured surface;L'arithmétique sur une surface percée

Annales des Telecommunications/Annals of Telecommunications

Volumn 51, Issue 7-8, 1996, Pages 407-420

  Perrine, Serge ^a  

^a Direction de Metz   (France)

Author keywords

Approximation; Arithmetic; Diophantine equation; Group theory; Non Euclidien geometry; Quadratic form; Rational number; Real number; Riemann geometry; Surface

Indexed keywords

EID: 3743094983     PISSN: 00034347     EISSN: 19589395     Source Type: Journal    
DOI: None     Document Type: Article

References (49)

1. MARKOFF (A. A.). Sur les formes quadratiques binaires indéfinies. Mathematische Annalen, Band VI, pp. 381-406 (1879). Band XVIII, pp. 379-399 (1880).
2. MARKOFF (A. A.). Sur les formes quadratiques binaires indéfinies. Mathematische Annalen, Band VI, pp. 381-406 (1879). Band XVIII, pp. 379-399 (1880).
3. CASSELS (J. W. S.). An introduction to diophantine approximation. Cambridge tracts in Mathematics and Mathematical Physics (1957), no 45.
4. DAS (A.). Integrable models. World Scientific Lectures Notes in Physics. World Scientific Publishing Co-Singapore (1989), 30.
5. HATA (M.). Legendre type polynomials and irrationality measures. J. Reine Angew. Math. (1990), 407, p. 99-125.
6. BORWEIN (J. M.), BORWEIN (P. B.). Pi and the AGM. John Wiley.
7. CHURCH HOUSE (R. F.), MUIR (S. T. E.). Continued fractions, algebraic numbers and modular invariants. J. Inst. Maths Applies (1969), 5, p. 318-328.
8. VAN DER POORTEN (A. J.). Remarks in the continued fractions of algebraic numbers. Publications mathématiques d'Orsay. Groupe de travail en théorie analytique et élémentaire des nombres (1986-1987).
9. PERRINE (S.). Approximation diophantienne (théorie de Markoff). Thèse présentée à l'Université de Metz (déc. 1988).
10. CUSICK (T. W.), FLAHIVE (M. E.). The Markoff and Lagrange spectra. Mathematical Surveys and Monographs. Amer. Math. Soc. Providence Ri (1989), 30.
11. MANNEVILLE (P.). Structures dissipatives, chaos et turbulence. Aléa, Saclay (1990).
12. COXETER (H. S. M.), MOSER (W. O. J.). Generators and relations for discrete groups. Springer Verlag (1980).
13. NEWMAN (M.). Integral matrices. Academic Press (1972).
14. COHN (H.). Approach to Markoff's minimal forms through modular functions. Annals of mathematics (Jan. 1955), 61, no 1, pp. 1-12.
15. PERRINE (S.). La méthode de Poincaré appliquée à l'arithmétique. Congrès international Henri Poincaré, Nancy (14-18 mai 1994).
16. BOURGNE (R.), AZRA (J. P.). Ecrits et mémoires d'Evariste Galois. Gauthiers Villars, Paris (1962), p. 365.
17. PERRINE (S.). Sur une généralisation de la théorie de Markoff. Journal of number Theory (fév. 1991), 37, no 2, pp. 211-230.
18. KLEIN (F.). Uber eine geometrische Auffassung des Gewöhnlichen Kettenbruchen. Nachr. Gres. Wiss. Göttingen (1985), p. 357.
19. GAUSS (C. F.). Disquisitiones arithmeticae (réédition Albert Blanchard).
20. SERRE (J. P.). Cours d'arithmétique. PUF, Paris (1970).
21. SARNAK (P.). Class numbers of indefinite binary quadratic forms. Journal of Number Theory 15 (1982), pp. 229-247.
22. BEDFORD (T.), KEANE (M.), SERIES (C.). Ergodic theory, symbolic dynamics and hyperbolic spaces. Oxford University Press (1991).
23. BESTVINA (M.), HANDEL (M.). Train tracks and automorphisms of free groups. Annals of Mathematics (1992), 135, pp. 1-13.
24. 2. Astérisque 46 SMF (1983).
25. PAULIN (F.). Actions de groupes sur les arbres. Séminaire Bourbaki (1995-1996), 48, no 808.
26. FATHI (A.), LAUDENBACH (F.), POENARU (V.). Travaux de Thurston sur les surfaces. Séminaire Orsay Astérisque (1991), no 66-67.
27. 1 factors of fuchsian groups. Astérisque (1996).
28. MASKIT (B.). On Poincaré's theorem for fundamental polygons. Advances in Math. (1971), 7, pp. 219-230.
29. SCHLICHENMAIER (M.). An introduction to Riemann surfaces, algebraic curves and moduli spaces. Lecture Notes in Physics no 322, Springer Verlag.
30. KERCKHOFF (S. P.). The Nielsen realization problem. Annals of Mathematics (1983), 117, pp. 235-265.
31. KEEN (L.). On Fricke moduli. Advances in the theory of Riemann surfaces. Ann. of Math. Studies (1966), pp. 205-215.
32. BESTVINA (M.), HANDEL (M.). Train-tracks for surface homeomorphism. Topology (1995), 34, no 1, pp. 109-140.
33. ANOSOV (D. V), ARNOLD (V. I.). Dynamical systems I. Springer Verlag.
34. LA HARPE (P. de). Operator algebras, free groups and other groups. Astérisque (1996).
35. CONNES (A.). Géométrie non commutative. Inter éditions (1990).
36. BERNARDETE (D.), NITECKI (Z.), GUTIERREZ (M.). Braids and the Nielsen Thurston classification. Journal of Knot Theory and its Ramifications (1995), 4, no 4, pp. 549-618.
37. JONES (V. F. R.). A polynomial invariant via Von Neumann algebra. Bull. Amer. Math. Soc. (Jan. 1985), 12, no 1, pp. 103-111.
38. HATCHER (A.). Homological stability for automorphism groups of free groups. Comment. Math. Helvetici (1995), 70, p. 39-62.
39. GROTHENDIECK (A.). Esquisse d'un programme (Jan. 1984).
40. WITTEN (E.). Physics and geometry. Proceedings of the international congress of mathematicians, Berkeley (1986).
41. ZUBER (J. P.). L'invariance conforme et la physique à deux dimensions. La Recherche (fév. 1993), 26, no 251.
42. GRANDATI (Y.). Eléments d'introduction à l'invariance conforme. Centre de Recherches Nucléaires de Strasbourg. Document CRN=PHTH/91-13.
43. NAKAHARA (M.). Geometry, topology and physics. IOP Publishing limited, London (1990).
44. WITTEN (E.). Quantum field theory and the Jones phynomial. Comm. Math. Phys. (1989), 121, pp. 351-399.
45. ATIYAH (M.). The geometry of physics of Knots. Cambridge University Press (1990).
46. DOUADY (R. et A.). Algèbre et théorie galoisiennes (tome 2). Cedic Nathan, Paris (1979).
47. GODBILLON (C.). Eléments de topologie algébrique. Hermann, Paris (1971).
48. POLLINGTON (A. D.), MORAN (W.). Lecture notes in pure and applied mathematics. Vol. 147, M. Dekker (1993).
49. SCHMUTZ (P.). Systoles of arithmetic surfaces and the Markoff spectrum. Math. Ann. (1996), 305, pp. 191-203.