publication . Article . Preprint . 2013

Landen transforms as families of (commuting) rational self-maps of projective space

Joseph Silverman;
  • Published: 24 Aug 2013
Abstract
Comment: 35 pages
Subjects
free text keywords: Mathematics - Algebraic Geometry, Mathematics - Dynamical Systems, Mathematics - Number Theory, Primary: 14E05, Secondary: 37P05
Related Organizations
Funded by
NSF| FRG: Collaborative Research: Algebraic Dynamics
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 0854755
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
25 references, page 1 of 2

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[2] G. Boros, M. Joyce, and V. H. Moll. A transformation of rational functions. Elem. Math., 58(2):73-83, 2003. [OpenAIRE]

[3] G. Boros, J. Little, V. Moll, E. Mosteig, and R. Stanley. A map on the space of rational functions. Rocky Mountain J. Math., 35(6):1861-1880, 2005.

[4] G. Boros and V. H. Moll. A rational Landen transformation. The case of degree six. In Analysis, geometry, number theory: the mathematics of Leon Ehrenpreis (Philadelphia, PA, 1998), volume 251 of Contemp. Math., pages 83-91. Amer. Math. Soc., Providence, RI, 2000.

[5] G. Boros and V. H. Moll. Landen transformations and the integration of rational functions. Math. Comp., 71(238):649-668 (electronic), 2002.

[6] S. Briscoe, L. Jiminez, D. Manna, L. Medina, and V. Moll. The dynamics of a transformation on the space of rational maps. in preparation.

[7] S. Cantat. Sur les groupes de transformations birationnelles des surfaces. Ann. of Math. (2), 174(1):299-340, 2011. [OpenAIRE]

[8] M. Chamberland and V. H. Moll. Dynamics of the degree six Landen transformation. Discrete Contin. Dyn. Syst., 15(3):905-919, 2006.

[9] T.-C. Dinh. Sur les applications de Latt`es de Pk. J. Math. Pures Appl. (9), 80(6):577-592, 2001.

[10] T.-C. Dinh. Sur les endomorphismes polynomiaux permutables de C2. Ann. Inst. Fourier (Grenoble), 51(2):431-459, 2001.

[11] T.-C. Dinh and N. Sibony. Sur les endomorphismes holomorphes permutables de Pk. Math. Ann., 324(1):33-70, 2002.

[12] C. F. Gauß. Arithmetische Geometrisches Mittel, 1799, Werke. Band III, pages 361-432. Konigliche Gesellschaft der Wissenschaft, Gottingen. Reprinted by Georg Olms Verlag, Hildesheim, 1973.

[13] J. Hubbard and V. Moll. A geometric view of rational Landen transformations. Bull. London Math. Soc., 35(3):293-301, 2003.

[14] 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, 61:298-309, 1771.

[15] 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, 65:283-289, 1775.

25 references, page 1 of 2
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publication . Article . Preprint . 2013

Landen transforms as families of (commuting) rational self-maps of projective space

Joseph Silverman;