Dynamics of the degree six landen transformation

Discrete and Continuous Dynamical Systems

Volumn 15, Issue 3, 2006, Pages 905-919

  Chamberland, Marc ^a   Moll, Victor H ^b  

^a GRINNELL COLLEGE   (United States)

^b Tulane University   (United States)

Author keywords

Dimension theory; Multifractal analysis; Poincare recurrences

Indexed keywords

EID: 33750411167     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2006.15.905     Document Type: Article

References (8)

1. G. Boros and V. Moll, A rational Landen transformation. The case of degree six. Contemporary Mathematics, 251 (2000), 83-91.
2. G. Boros and V. Moll, Landen transformation and the integration of rational function. Math. Comp., 71 (2001), 649-668.
3. J. M. Borwein and P. Borwein, Pi and the AGM. John Wiley and Sons, 1987
4. . [4] K. F. Gauss, Arithmetische Geometrisches Mittel, (1799). In Werke, 3, 361-432. Konigliche Gesellschaft der Wissenschaft, Gottingen. Reprinted by Olms, Hildescheim, 1981.
5. J. Hubbard and V. Moll, A geometric view of the rational Landen transformation. Bull. London Math. Soc., 35 (2003), 293-301.
6. J. Landen, A disquisition concerning certain fluents, which are assignable by the arcs of the conic sections; wherein are investigated some new and useful theorems for computing such fluents. Philos. Trans. Royal Soc. London, 61 (1771), 298-309.
7. J. Landen, An investigation of a general theorem for finding the length of any arc of any conic hyperbola, by means of two elliptic arcs, with some other new and useful theorems deduced therefrom. Philos. Trans. Royal Soc. London, textbf65 (1775), 283-289.
8. Ṡ. I. Pinchuk, Counterexample to the Strong Real Jacobian Conjecture. Math. Z., 217 (1994), 1-4.