Hausdorff dimension of subsets of the parameter space for families of rational maps. (A generalization of Shishikura's result)

Nonlinearity

Volumn 11, Issue 2, 1998, Pages 233-246

  Tan, Lei ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040944223     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/11/2/003     Document Type: Article

References (13)

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4. Douady A and Hubbard J 1985 On the dynamics of polynomial-like mappings Ann. Sci. Ec. Norm. Sup. 18 287-343
5. Falconer K 1990 Fractal Geometry (New York: Wiley)
6. Lavaurs P 1989 Systèmes dynamiques holomorphes, explosion de points périodiques paraboliques Thèse de Doctorat l'Université de Paris-Sud, Orsay, France
7. McMullen C 1994 Complex Dynamics and Renormalization (Ann. Math. Studies 135) (Princeton, NJ: Princeton University Press)
8. McMullen C 1997 The Mandelbrot set is universal Preprint
9. Mañé R, Sad P and Sullivan D 1983 On the dynamics of rational maps Ann. Sci. Ec. Norm. Sup. 16 193-217
10. Rees M 1986 Positive measure sets of ergodic rational maps Ann. Sci. Ec. Norm. Sup. 19 383-407
11. Shishikura M 1991 The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets Preprint SUNY Stony Brook 1991/7
12. Shishikura M 1993 The parabolic bifurcation of rational maps, 19° Colóquio Brasileiro de Matemática, IMPA
13. Shishikura M 1994 The boundary of the Mandelbrot set has Hausdorff dimension two, S.M.F. Astérisque vol 222 pp 389-405