Bibliography for Julia Sets

short

 

  1. Some geometric properties of Julia sets and filled-in Julia sets of polynomials.
    Yang, Guoxiao
    Complex Var. Theory Appl. 47 (2002), no. 5, 383--391, MathSciNet.  
  2. Mandelbrot sets for Julia sets in the general case. The Mandelbrot sets for Julia sets of high order.
    Tomova, A.
    Applications of mathematics in engineering and economics (Sozopol, 2001), 323--334, Heron Press, Sofia, 2002, MathSciNet.  
  3. Julia sets for the super-Newton method, Cauchy's method, and Halley's method.
    Kneisl, Kyle
    Chaos 11 (2001), no. 2, 359--370, MathSciNet.  
  4. Geometric properties of Julia sets of the composition of polynomials of the form z^2+c^ n.
    Brück, Rainer
    Pacific J. Math. 198 (2001), no. 2, 347--372, MathSciNet.  
  5. The Julia set of a random iteration system.
    Zhou, Ji
    Bull. Austral. Math. Soc. 62 (2000), no. 1, 45--50, MathSciNet.  
  6. Local connectivity of Julia sets: expository lectures.  
    Milnor, John
    The Mandelbrot set, theme and variations,  67--116, London Math. Soc. Lecture Note Ser., 274, Cambridge Univ. Press, Cambridge, 2000, MathSciNet.  
  7. A study of Mandelbrot and Julia sets generated from a general complex cubic iteration.
    Yan, Dejun; Liu, Xiangdong; Zhu, Weiyong
    Fractals 7 (1999), no. 4, 433--437, MathSciNet.  
  8. Analytical study of the Julia set of a coupled generalized logistic map.
    Yoshida, Katsuhiko; Saito, Satoru
    J. Phys. Soc. Japan 68 (1999), no. 5, 1513--1525, MathSciNet.  
  9. Simple proofs of some fundamental properties of the Julia set.
    Bargmann, Detlef
    Ergodic Theory Dynam. Systems 19 (1999), no. 3, 553--558, MathSciNet.  
  10. Physical meaning for Mandelbrot and Julia sets.
    Beck, Christian
    Phys. D 125 (1999), no. 3-4, 171--182, MathSciNet.  
  11. Julia sets of skew products in C2.
    Heinemann, Stefan-M.
    Kyushu J. Math. 52 (1998), no. 2, 299--329, MathSciNet.  
  12. Julia sets in Cn.
    Heinemann, Stefan-M.
    Progress in holomorphic dynamics, 159--185, Pitman Res. Notes Math. Ser., 387, Longman, Harlow, 1998, MathSciNet.  
  13. Local connectedness of the Julia set of the family z^m (z^n-b).  
    Rabii, Maryam
    Ergodic Theory Dynam. Systems  18  (1998),  no. 2, 457--470, MathSciNet.  
  14. When do Two Rational Functions Have the Same Julia Set?  
    G. Levin; F. Przytycki  
    Proceedings of the American Mathematical Society, Vol. 125, No. 7. (Jul., 1997), pp. 2179-2190, Jstor.  
  15. Not all Julia Sets are Quasi-Self-Similar  
    Pentti Jarvi  
    Proceedings of the American Mathematical Society, Vol. 125, No. 3. (Mar., 1997), pp. 835-837, Jstor.  
  16. Chebyshev polynomials on equipotential curves of a quadratic Julia set.
    Stawiska, Magorzata
    Univ. Iagel. Acta Math. No. 33 (1996), 191--198, MathSciNet.  
  17. Julia sets and non-constant limits in the composition of entire functions.
    Maalouf, Ramez N.
    Complex Variables Theory Appl. 30 (1996), no. 2, 97--112, MathSciNet.  
  18. Local connectivity of some Julia sets containing a circle with an irrational rotation.
    Petersen, Carsten Lunde
    Acta Math. 177 (1996), no. 2, 163--224, MathSciNet.  
  19. On the Julia set of polynomials with complex coefficients.
    Bhattacharyya, P.; Tamil Durai, M.
    J. Math. Phys. Sci. 29 (1995), no. 3, 119--129, MathSciNet.  
  20. The polynomials associated with a Julia set.
    Schmidt, W.; Steinmetz, N.
    Bull. London Math. Soc. 27 (1995), no. 3, 239--241, MathSciNet.  
  21. Topological, geometric and complex analytic properties of Julia sets.
    Shishikura, Mitsuhiro
    Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), 886--895, Birkhäuser, Basel, 1995, MathSciNet.  
  22. Positive reducibility of the interior of filled Julia sets.
    Chong, C. T.
    J. Complexity 10 (1994), no. 4, 437--444, MathSciNet.  
  23. The Geometry of Julia Sets  
    Jan M. Aarts; Lex G. Oversteegen  
    Transactions of the American Mathematical Society, Vol. 338, No. 2. (Aug., 1993), pp. 897-918, Jstor.  
  24. Julia Sets and Differential Equations  
    Harold E. Benzinger  
    Proceedings of the American Mathematical Society, Vol. 117, No. 4. (Apr., 1993), pp. 939-946, Jstor.  
  25. Indecomposable Continua and the Julia Sets of Polynomials  
    John C. Mayer; James T. Rogers, Jr.  
    Proceedings of the American Mathematical Society, Vol. 117, No. 3. (Mar., 1993), pp. 795-802, Jstor.  
  26. Julia sets and differential equations.
    Benzinger, Harold E.
    Proc. Amer. Math. Soc. 117 (1993), no. 4, 939--946, MathSciNet.  
  27. The geometry of Julia sets.
    Aarts, Jan M.; Oversteegen, Lex G.
    Trans. Amer. Math. Soc. 338 (1993), no. 2, 897--918, MathSciNet.  
  28. Julia Sets are Uniformly Perfect  
    R. Mane; L. F. Da Rocha  
    Proceedings of the American Mathematical Society, Vol. 116, No. 1. (Sep., 1992), pp. 251-257, Jstor.  
  29. Taylor series approximations to Julia set scaling functions.
    Osbaldestin, A. H.; Sarkis, M. Y.
    Phys. D 57 (1992), no. 3-4, 330--336, MathSciNet.  
  30. On the quaternionic Julia sets.
    Petek, Peter
    Chaotic dynamics (Patras, 1991), 53--58, NATO Adv. Sci. Inst. Ser. B Phys., 298, Plenum, New York, 1992, MathSciNet.  
  31. The components of a Julia set.
    Beardon, A. F.
    Ann. Acad. Sci. Fenn. Ser. A I Math. 16 (1991), no. 1, 173--177, MathSciNet.  
  32. Julia sets for the gamma recursion in nonlinear psychophysics.  
    Campbell, Edward A.; Gregson, Robert A. M.
    Acta Appl. Math.  20  (1990),  no. 1-2, 177--188, MathSciNet.  
  33. Orthogonal polynomials, Padé approximations and Julia sets.
    Bessis, D.
    Orthogonal polynomials (Columbus, OH, 1989), 55--97, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 294, Kluwer Acad. Publ., Dordrecht, 1990, MathSciNet.  
  34. Analytic evaluation of the multifractal properties of a Newtonian Julia set.
    Nauenberg, M.; Schellnhuber, H. J.
    Phys. Rev. Lett. 62 (1989), no. 16, 1807--1810, MathSciNet.  
  35. Ramanujan and the Julia set of the iterated exponential map.
    Lakhtakia, Akhlesh; Lakhtakia, Mercedes
    Z. Naturforsch. A 43 (1988), no. 7, 681--683, MathSciNet.  
  36. A problem on Julia sets.
    Baker, I. N.; Erëmenko, A.
    Ann. Acad. Sci. Fenn. Ser. A I Math. 12 (1987), no. 2, 229--236, MathSciNet.  
  37. Efficient computation of Julia sets and their fractal dimension.
    Saupe, Dietmar
    Phys. D 28 (1987), no. 3, 358--370, MathSciNet.  
  38. Area and Hausdorff Dimension of Julia Sets of Entire Functions  
    Curt McMullen  
    Transactions of the American Mathematical Society, Vol. 300, No. 1. (Mar., 1987), pp. 329-342, Jstor.  
  39. Julia Sets and Mandelbrot-Like Sets Associated With Higher Order Schroder Rational Iteration Functions: A Computer Assisted Study  
    Edward R. Vrscay  
    Mathematics of Computation, Vol. 46, No. 173. (Jan., 1986), pp. 151-169, Jstor.  
  40. Julia sets and Mandelbrot-like sets associated with higher order Schröder rational iteration functions: a computer assisted study.
    Math. Comp. 46 (1986), no. 173, 151--169, MathSciNet.  
    Vrscay, Edward R.
  41. Quasiconformal Homeomorphisms and Dynamics I. Solution of the Fatou-Julia Problem on Wandering Domains  
    Dennis Sullivan  
    The Annals of Mathematics, 2nd Ser., Vol. 122, No. 2. (Sep., 1985), pp. 401-418, Jstor.
  42. Condensed Julia Sets, with an Application to a Fractal Lattice Model Hamiltonian  
    M. F. Barnsley; J. S. Geronimo; A. N. Harrington  
    Transactions of the American Mathematical Society, Vol. 288, No. 2. (Apr., 1985), pp. 537-561, Jstor.
  43. A new real space renormalisation method and its Julia set.
    Derrida, B.; Flyvbjerg, H.
    J. Phys. A 18 (1985), no. 6, L313--L318, MathSciNet.  
  44. Phase transitions and Julia sets.
    Peitgen, H.-O.; Prüfer, M.; Richter, P. H.
    Lotka-Volterra-approach to cooperation and competition in dynamic systems (Eisenach, 1984), 81--102, Math. Res., 23, Akademie-Verlag, Berlin, 1985, MathSciNet.  
  45. Shorter Notes: Erratum to "Infinite-Dimensional Jacobi Matrices Associated with Julia Sets"  
    M. F. Barnsley; J. S. Geronimo; A. N. Harrington  
    Proceedings of the American Mathematical Society, Vol. 92, No. 1. (Sep., 1984), p. 156, Jstor.
  46. Moments of Balanced Measures on Julia Sets  
    M. F. Barnsley; A. N. Harrington  
    Transactions of the American Mathematical Society, Vol. 284, No. 1. (Jul., 1984), pp. 271-280, Jstor.
  47. Cayley's Problem and Julia Sets  
    Peitgen, H. O. and D. Saupe and F. V. Haeseler  
    Math. Intell., (1984), V. 6, No. 2, pp. 11-20.  
  48. Julia sets and bifurcation diagrams for exponential maps.
    Devaney, Robert L.
    Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 1, 167--171, MathSciNet.  
  49. Infinite-Dimensional Jacobi Matrices Associated with Julia Sets  
    M. F. Barnsley; J. S. Geronimo; A. N. Harrington  
    Proceedings of the American Mathematical Society, Vol. 88, No. 4. (Aug., 1983), pp. 625-630, Jstor.
  50. Every Direction a Julia Direction  
    Bryan E. Cain  
    Proceedings of the American Mathematical Society, Vol. 46, No. 2. (Nov., 1974), pp. 250-252, Jstor.
  51. On Julia's Corollary to Picard's Great Theorem (in Classroom Notes)  
    J. W. Macki  
    The American Mathematical Monthly, Vol. 75, No. 6. (Jun. - Jul., 1968), pp. 655-656, Jstor.

 

 

 

 Return to the Complex Analysis Project

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003