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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Orthogonal polynomials associated with invariant measures on Julia sets


Authors: M. F. Barnsley, J. S. Geronimo and A. N. Harrington
Journal: Bull. Amer. Math. Soc. 7 (1982), 381-384
MSC (1980): Primary 42A52
MathSciNet review: 663789
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  • 1. M. F. Barnsley, J. S. Geronimo, and A. N. Harrington, On the invariant sets of a family of quadratic maps, Comm. Math. Phys. 88 (1983), no. 4, 479–501. MR 702565 (85g:58055)
  • 2. M. F. Barnsley, J. S. Geronimo and A. N. Harrington (in preparation)
  • 3. D. Bessis, M. L. Mehta, and P. Moussa, Orthogonal polynomials on a family of Cantor sets and the problem of iterations of quadratic mappings, Letters in Math. Phys. (submitted).
  • 4. Hans Brolin, Invariant sets under iteration of rational functions, Ark. Mat. 6 (1965), 103–144 (1965). MR 0194595 (33 #2805)
  • 5. P. Fatou, Sur les équations fonctionnelles, Bull. Soc. Math. France 47 (1919), 161–271 (French). MR 1504787
  • 6. H. Brolin, Sur les équations fonctionelles, Bull. Soc. Math. France 48 (1920), 33-94; 208-314.
  • 7. Lisl Gaal, Classical Galois theory with examples, Markham Publishing Co., Chicago, Ill., 1971. MR 0280465 (43 #6185)
  • 8. G. Julia, Mémoire sur L'iteration des fonctions rationelles, J. Math. Pures Appl. Ser. 8 1 (1918), 47-245.
  • 9. V. J. Smirnoff, Sur les formules de Cauchy et de Green quelques problemes qui s'y rattachent, Bull. Acad. Sci. URSS (1932), 337-372.
  • 10. Gábor Szegő, Orthogonal polynomials, 3rd ed., American Mathematical Society, Providence, R.I., 1967. American Mathematical Society Colloquium Publications, Vol. 23. MR 0310533 (46 #9631)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1982-15043-1
PII: S 0273-0979(1982)15043-1