Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Linear independence of iterates and entire solutions of functional equations

Authors: Jens Peter Reus Christensen and Pal Fischer
Journal: Proc. Amer. Math. Soc. 103 (1988), 1120-1124
MSC: Primary 30D05; Secondary 30D20, 39B10
MathSciNet review: 954993
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A classical result of Pólya concerning the growth of Nevanlinna's characteristics of composite functions is used to prove linear independence of some iterates. The same result of Pólya is also used to show the nonexistence of entire solutions of the Feigenbaum functional equation.

References [Enhancements On Off] (What's this?)

  • [1] M. Cosnard, Étude des solutions de l'équation de Feigenbaum, Astérisque 98-99 (1982), 143-162. MR 724445 (85f:58083)
  • [2] P. Fischer, Feigenbaum functional equation and periodic points, Aequationes Math. 30 (1986), 202-207. MR 843661 (87k:58216)
  • [3] -, Feigenbaum functional equations as dynamical systems, Chaos, Fractals, and Dynamics (P. Fischer and W. R. Smith, eds.), Dekker, 1985, pp. 183-188. MR 813518 (87d:58076)
  • [4] -, On the general unimodal solution of the Feigenbaum functional equation and related classes of solutions (to appear).
  • [5] V. Ganapathy Iyer, On a functional equation. II, Indian J. Math. 2 (1960), 1-7. MR 0111953 (22:2811)
  • [6] W. K. Hayman, Meromorphic functions, Oxford Mathematical Monograph, Oxford at the Clarendon Press, 1964. MR 0164038 (29:1337)
  • [7] O. E. Lanford III, Smooth transformations of intervals, Séminaire Bourbaki, 1980/81, Lecture Notes in Math., vol. 901, Springer-Verlag, Berlin and New York, 1981, pp. 36-54. MR 647487 (83k:58066)
  • [8] -, A computer-assisted proof of the Feigenbaum conjectures, Bull. Amer. Math. Soc. (N.S.) 6 (1982), 427-434. MR 648529 (83g:58051)
  • [9] G. Pólya, On an integral function of an integral function, J. London Math. Soc. 1 (1926), 12-15.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30D05, 30D20, 39B10

Retrieve articles in all journals with MSC: 30D05, 30D20, 39B10

Additional Information

Keywords: Nevanlinna's characteristic, linear independence of iterates, Feigenbaum functional equation
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society