Bibliography for Julia Sets

unabridged

 

  1. Calculating Hausdorff Dimension of Julia Sets and Kleinian Limit Sets  
    Oliver Jenkinson; Mark Pollicott  
    American Journal of Mathematics, Vol. 124, No. 3. (Jun., 2002), pp. 495-545, Jstor.  
  2. Julia set describes quantum tunnelling in the presence of chaos
    Shudo A.; Ishii Y.; Ikeda K.S.
    Journal of Physics A: Mathematical and General, 2002, vol. 35, no. 17, pp. L225-L231(1), Ingenta.  
  3. Parametric 2-dimensional L systems and recursive fractal images: Mandelbrot set, Julia sets and biomorphs
    Ortega A.; de la Cruz M.; Alfonseca M.
    Computers and Graphics, February 2002, vol. 26, no. 1, pp. 143-149(7), Ingenta.  
  4. Julia set describes quantum tunnelling in the presence of chaos.  
    Shudo, A.; Ishii, Y.; Ikeda, K. S.
    J. Phys. A  35  (2002),  no. 17, L225--L231, MathSciNet.  
  5. Some properties of Fatou and Julia sets of transcendental meromorphic functions.
    Zheng, Jian-Hua; Wang, Sheng; Huang, Zhi-Gang
    Bull. Austral. Math. Soc. 66 (2002), no. 1, 1--8, MathSciNet.  
  6. 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.  
  7. On dynamics of vertices of locally connected polynomial Julia sets.
    Blokh, A.; Levin, G.
    Proc. Amer. Math. Soc. 130 (2002), no. 11, 3219--3230 (electronic), MathSciNet.  
  8. 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.  
  9. Geometric exponents for hyperbolic Julia sets.
    Heinemann, Stefan-M.; Stratmann, Bernd O.
    Illinois J. Math. 45 (2001), no. 3, 775--785, MathSciNet.  
  10. Accessible points in the Julia sets of stable exponentials.
    Bhattacharjee, Ranjit; Devaney, Robert L.; Deville, R. E. Lee; Josi'c, Kresimir; Moreno-Rocha, Monica
    Discrete Contin. Dyn. Syst. Ser. B 1 (2001), no. 3, 299--318, MathSciNet.  
  11. On the continuity of Hausdorff dimension of Julia sets and similarity between the Mandelbrot set and Julia sets.
    Rivera-Letelier, Juan
    Fund. Math. 170 (2001), no. 3, 287--317, MathSciNet.  
  12. Julia sets for the super-Newton method, Cauchy's method, and Halley's method.
    Kneisl, Kyle
    Chaos 11 (2001), no. 2, 359--370, MathSciNet.  
  13. On the connectivity of the Julia set of a finitely generated rational semigroup.
    Sun, Yeshun; Yang, Chung-Chun
    Proc. Amer. Math. Soc. 130 (2002), no. 1, 49--52 (electronic), MathSciNet.  
  14. 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.  
  15. Julia sets in parameter spaces.
    Buff, X.; Henriksen, C.
    Comm. Math. Phys. 220 (2001), no. 2, 333--375, MathSciNet.  
  16. Erratum to ''On the Julia set of the perturbed Mandelbrot map'' [Chaos, Solitons & Fractals 11 (2001) 2067-2073]
    Argyris J.; Karakasidis T.E.; Andreadis I.
    Chaos, Solitons and Fractals, 1 January 2001, vol. 12, no. 1, pp. 196-196(1), Ingenta.  
  17. On supports of dynamical laminations and biaccessible points in polynomial Julia sets.
    Smirnov, Stanislav K.
    Colloq. Math. 87 (2001), no. 2, 287--295, MathSciNet.  
  18. Renormalization group method and Julia sets.
    Abdusalam, H. A.
    Chaos Solitons Fractals 12 (2001), no. 2, 423--428, MathSciNet.  
  19. On the Julia set of the perturbed Mandelbrot map
    Argyris J.; Karakasidis T.E.; Andreadis I.
    Chaos, Solitons and Fractals, October 2000, vol. 11, no. 13, pp. 2067-2073(7), Ingenta.  
  20. Dimension of Julia sets of polynomial automorphisms of C2.
    Wolf, Christian
    Michigan Math. J. 47 (2000), no. 3, 585--600, MathSciNet.  
  21. On biaccessible points in Julia sets of polynomials.
    Zdunik, Anna
    Fund. Math. 163 (2000), no. 3, 277--286, MathSciNet.  
  22. The Julia set of a random iteration system.
    Zhou, Ji
    Bull. Austral. Math. Soc. 62 (2000), no. 1, 45--50, MathSciNet.  
  23. On biaccessible points in the Julia set of a Cremer quadratic polynomial.
    Schleicher, Dierk; Zakeri, Saeed
    Proc. Amer. Math. Soc. 128 (2000), no. 3, 933--937, MathSciNet.  
  24. 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.  
  25. Une démonstration directe de la densité des cycles répulsifs dans l'ensemble de Julia. (French) [A direct proof of the density of repulsive cycles in a Julia set]
    Berteloot, François; Duval, Julien
    Complex analysis and geometry (Paris, 1997), 221--222, Progr. Math., 188, Birkhäuser, Basel, 2000, MathSciNet.  
  26. 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.  
  27. Random iterations of polynomials of the form z^2+c^n: connectedness of Julia sets.
    Brück, Rainer; Büger, Matthias; Reitz, Stefan
    Ergodic Theory Dynam. Systems 19 (1999), no. 5, 1221--1231, MathSciNet.  
  28. 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.  
  29. Continuity of Julia sets.
    Wu, Shengjian
    Sci. China Ser. A 42 (1999), no. 3, 281--285, MathSciNet.  
  30. Porosity of parabolic Julia sets.
    Geyer, Lukas
    Complex Variables Theory Appl. 39 (1999), no. 3, 191--198, MathSciNet.  
  31. Simple proofs of some fundamental properties of the Julia set.
    Bargmann, Detlef
    Ergodic Theory Dynam. Systems 19 (1999), no. 3, 553--558, MathSciNet.  
  32. Area and Hausdorff dimension of the set of accessible points of the Julia sets of lambda e^z and lambda sin z.
    Karpi'nska, Bogusawa
    Fund. Math. 159 (1999), no. 3, 269--287, MathSciNet.  
  33. Completely invariant Julia sets of polynomial semigroups.
    Stankewitz, Rich
    Proc. Amer. Math. Soc. 127 (1999), no. 10, 2889--2898, MathSciNet.  
  34. Physical meaning for Mandelbrot and Julia sets.
    Beck, Christian
    Phys. D 125 (1999), no. 3-4, 171--182, MathSciNet.  
  35. Multifractal dimensions and thermodynamical description of nearly-circular Julia sets.
    Abenda, Simonetta; Moussa, Pierre; Osbaldestin, Andrew H.
    Nonlinearity 12 (1999), no. 1, 19--40, MathSciNet.  
  36. On the topology of Julia sets.
    Postolache, M.; Ciobanu, E.
    Proceedings of the Workshop on Global Analysis, Differential Geometry, Lie Algebras (Thessaloniki, 1996), 78--85, BSG Proc., 3, Geom. Balkan Press, Bucharest, 1999, MathSciNet.  
  37. Fraktale und Julia-Mengen. (German) [Fractals and Julia sets] With 1 CD-ROM (Windows).
    Dufner, J.; Roser, A.; Unseld, F.
    Verlag Harri Deutsch, Thun, 1998. viii+288 pp. ISBN: 3-8171-1564-4, MathSciNet.  
  38. The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets.
    Shishikura, Mitsuhiro
    Ann. of Math. (2) 147 (1998), no. 2, 225--267, MathSciNet.  
  39. On Hausdorff dimension of Julia sets of hyperbolic rational semigroups.
    Sumi, Hiroki
    Kodai Math. J. 21 (1998), no. 1, 10--28, MathSciNet.  
  40. Julia sets of skew products in C2.
    Heinemann, Stefan-M.
    Kyushu J. Math. 52 (1998), no. 2, 299--329, MathSciNet.  
  41. Julia sets in Cn.
    Heinemann, Stefan-M.
    Progress in holomorphic dynamics, 159--185, Pitman Res. Notes Math. Ser., 387, Longman, Harlow, 1998, MathSciNet.  
  42. Local connectivity of the Julia set of real polynomials.
    Levin, Genadi; van Strien, Sebastian
    Ann. of Math. (2) 147 (1998), no. 3, 471--541, MathSciNet.  
  43. 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.  
  44. On the connectivity of Julia sets of transcendental entire functions.
    Kisaka, Masashi
    Ergodic Theory Dynam. Systems 18 (1998), no. 1, 189--205, MathSciNet.  
  45. 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.  
  46. 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.  
  47. Topological complexity of Julia sets.
    Qiao, Jianyong
    Sci. China Ser. A 40 (1997), no. 11, 1158--1165, MathSciNet.  
  48. Some cubic Julia sets.
    Lee, Hung Hwan; Baek, Hun Ki
    Korean J. Comput. Appl. Math. 4 (1997), no. 1, 31--37, MathSciNet.  
  49. Chebyshev polynomials on equipotential curves of a quadratic Julia set.
    Stawiska, Magorzata
    Univ. Iagel. Acta Math. No. 33 (1996), 191--198, MathSciNet.  
  50. Hausdorff dimension of Julia sets of complex Hénon mappings.
    Verjovsky, A.; Wu, H.
    Ergodic Theory Dynam. Systems 16 (1996), no. 4, 849--861, MathSciNet.  
  51. Local connectivity of the Julia set for geometrically finite rational maps.
    Tan, Lei; Yin, Yongcheng
    Sci. China Ser. A 39 (1996), no. 1, 39--47, MathSciNet.  
  52. Julia sets of inner compositions.
    Maalouf, Ramez N.
    Arch. Math. (Basel) 67 (1996), no. 2, 138--141, MathSciNet.  
  53. 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.  
  54. 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.  
  55. The rigorous solutions of some nonlinear complex dynamical systems.
    Matayoshi, Gousirou; Matayoshi, Seitarou
    The filled Julia set and the Mandelbrot set. Bull. College Sci. Univ. Ryukyus No. 63 (1996), 63--71, MathSciNet.  
  56. Julia sets for complex dynamics on projective spaces.
    Ueda, Tetsuo
    Geometric complex analysis (Hayama, 1995), 629--633, World Sci. Publishing, River Edge, NJ, 1996, MathSciNet.  
  57. The buried points on the Julia sets of rational and entire functions.
    Qiao, Jianyong
    Sci. China Ser. A 38 (1995), no. 12, 1409--1419, MathSciNet.  
  58. Representations of the Whitehead manifold Wh3 and Julia sets.
    Poénaru, Valentin; Tanasi, Corrado
    Ann. Fac. Sci. Toulouse Math. (6) 4 (1995), no. 3, 655--694, MathSciNet.  
  59. The Hausdorff dimension of the Julia set for complex polynomial z^d+.
    Yang, Guo Xiao
    Chinese Sci. Bull. 40 (1995), no. 8, 617--620, MathSciNet.  
  60. 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.  
  61. Continuity of Julia sets of polynomials. (Chinese)
    Yin, Yong Cheng
    Acta Math. Sinica 38 (1995), no. 1, 99--102, MathSciNet.  
  62. A note on the Julia set of a rational function.
    Letherman, S. D.; Wood, R. M. W.
    Math. Proc. Cambridge Philos. Soc. 118 (1995), no. 3, 477--485, MathSciNet.  
  63. Ising models, Julia sets, and similarity of the maximal entropy measures.
    Ishii, Yutaka
    J. Statist. Phys. 78 (1995), no. 3-4, 815--825, MathSciNet.  
  64. The polynomials associated with a Julia set.
    Schmidt, W.; Steinmetz, N.
    Bull. London Math. Soc. 27 (1995), no. 3, 239--241, MathSciNet.  
  65. Local uniform convergence and convergence of Julia sets.  
    Kisaka, Masashi
    Nonlinearity  8  (1995),  no. 2, 273--281, MathSciNet.  
  66. Percolation and Julia sets.
    Ahmed, E.; Abdusalam, H. A.
    Internat. J. Theoret. Phys. 34 (1995), no. 2, 287--292, MathSciNet.  
  67. The polynomial topological complexity of Fatou-Julia sets.
    Chong, C. T.
    Adv. Comput. Math. 3 (1995), no. 4, 369--374, MathSciNet.  
  68. 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.  
  69. Symbolic dynamics for angle-doubling on the circle. IV. Equivalence of abstract Julia sets.
    Keller, Karsten
    Atti Sem. Mat. Fis. Univ. Modena 42 (1994), no. 2, 547--567, MathSciNet.  
  70. Positive reducibility of the interior of filled Julia sets.
    Chong, C. T.
    J. Complexity 10 (1994), no. 4, 437--444, MathSciNet.  
  71. Ising models, Julia sets and similarity of the maximal entropy measures.
    Ishii, Yutaka
    Geometry and analysis in dynamical systems (Kyoto, 1993), 1--12, Adv. Ser. Dynam. Systems, 14, World Sci. Publishing, River Edge, NJ, 1994, MathSciNet.  
  72. 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.  
  73. Julia Sets and Differential Equations  
    Harold E. Benzinger  
    Proceedings of the American Mathematical Society, Vol. 117, No. 4. (Apr., 1993), pp. 939-946, Jstor.  
  74. 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.  
  75. Julia sets and differential equations.
    Benzinger, Harold E.
    Proc. Amer. Math. Soc. 117 (1993), no. 4, 939--946, MathSciNet.  
  76. Griffin, C. J.; Joshi, G. C.
    Transition points in octonionic Julia sets.
    Chaos Solitons Fractals 3 (1993), no. 1, 67--88, MathSciNet.  
  77. Value distributions of entire functions and Julia sets. (Chinese)
    Qiao, Jian Yong
    Acta Math. Sinica 36 (1993), no. 3, 418--422, MathSciNet.  
  78. The geometry of Julia sets.
    Aarts, Jan M.; Oversteegen, Lex G.
    Trans. Amer. Math. Soc. 338 (1993), no. 2, 897--918, MathSciNet.  
  79. Local connnectivity of Julia sets and bifurcation loci: three theorems of J.-C. Yoccoz.
    Hubbard, J. H.
    Topological methods in modern mathematics (Stony Brook, NY, 1991), 467--511, Publish or Perish, Houston, TX, 1993, MathSciNet.  
  80. 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.  
  81. Julia set of the function z exp(z+µ).
    Jang, Cheol Min
    Tohoku Math. J. (2) 44 (1992), no. 2, 271--277, MathSciNet.  
  82. Taylor series approximations to Julia set scaling functions.
    Osbaldestin, A. H.; Sarkis, M. Y.
    Phys. D 57 (1992), no. 3-4, 330--336, MathSciNet.  
  83. Multifractal analysis of nearly circular Julia set and thermodynamical formalism.
    Collet, P.; Dobbertin, R.; Moussa, P.
    Ann. Inst. H. Poincaré Phys. Théor. 56 (1992), no. 1, 91--122, MathSciNet.  
  84. Julia sets and complex singularities in hierarchical Ising models.
    Bleher, P. M.; Lyubich, M. Yu.
    Comm. Math. Phys. 141 (1991), no. 3, 453--474, MathSciNet.  
  85. Fisher zeros and Julia sets: a multifractal analysis.
    Hu, Bambi; Lin, Bin
    Current problems in statistical mechanics (Washington, DC, 1991). Phys. A 177 (1991), no. 1-3, 38--44, MathSciNet.  
  86. 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.  
  87. The components of a Julia set.
    Beardon, A. F.
    Ann. Acad. Sci. Fenn. Ser. A I Math. 16 (1991), no. 1, 173--177, MathSciNet.  
  88. 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.  
  89. An explosion point for the set of endpoints of the Julia set of lambda exp(z).
    Mayer, John C.
    Ergodic Theory Dynam. Systems 10 (1990), no. 1, 177--183, MathSciNet.  
  90. 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.  
  91. 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.  
  92. Hausdorff dimension and dimension spectrum for Julia sets close to unit circle.
    Moussa, Pierre
    Nonlinear dynamics (Bologna, 1988), 88--108, World Sci. Publishing, Teaneck, NJ, 1989, MathSciNet.  
  93. Ramanujan and the Julia set of the iterated exponential map.
    Lakhtakia, Akhlesh; Lakhtakia, Mercedes
    Z. Naturforsch. A 43 (1988), no. 7, 681--683, MathSciNet.  
  94. 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.  
  95. Efficient computation of Julia sets and their fractal dimension.
    Saupe, Dietmar
    Phys. D 28 (1987), no. 3, 358--370, MathSciNet.  
  96. 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.  
  97. 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.  
  98. 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.
  99. 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.
  100. 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.
  101. A new real space renormalisation method and its Julia set.
    Derrida, B.; Flyvbjerg, H.
    J. Phys. A 18 (1985), no. 6, L313--L318, MathSciNet.  
  102. 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.  
  103. 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.
  104. 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.
  105. 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.  
  106. Julia sets and bifurcation diagrams for exponential maps.
    Devaney, Robert L.
    Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 1, 167--171, MathSciNet.  
  107. Mellin transforms associated with Julia sets and physical applications.
    Bessis, D.; Geronimo, J. S.; Moussa, P.
    J. Statist. Phys. 34 (1984), no. 1-2, 75--110, MathSciNet.  
  108. 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.
  109. Every Direction a Julia Direction  
    Bryan E. Cain  
    Proceedings of the American Mathematical Society, Vol. 46, No. 2. (Nov., 1974), pp. 250-252, Jstor.
  110. 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.

 

 

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