The exact Hausdorff dimension functions of some Cantor sets

Nonlinearity

Volumn 16, Issue 3, 2003, Pages 963-970

  Olsen, L ^a  

^a UNIVERSITY OF ST ANDREWS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242308838     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/3/309     Document Type: Article

References (16)

1. [BD] Bernik V and Dodson M 1999 Metric Diophantine Approximation on Manifolds (Cambridge Tracts in Mathematics vol 137) (Cambridge: Cambridge University Press)
2. [Ca] Carathéodory C1914 Über das lineare Maß von Punktmengen - eine Verallgemeinerung des Längenbegriffs Nachrichten der K. Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse, pp 404-26
3. [Co] Cooper M 1996 Dimension and measure defined by infinite Bernoulli convolutions PhD thesis University of London
4. [Ed] Edgar G 1992 Classics on Fractals (Menlo Park, CA: Addison-Wesley)
5. [Fa1] Falconer K J 1986 The Geometry of Fractal Sets (Cambridge Tracts in Mathematics vol 85) (Cambridge; Cambridge University Press)
6. [Fa2] Falconer K J 1990 Fractal Geometry - Mathematical Foundations and Applications (New York: Wiley)
7. [GMW] Graf S, Mauldin R D and Williams S 1988 The exact Hausdorff dimension in random recursive constructions Memoirs of the American Mathematical Society vol 71 (Providence, RI: American Mathematical Society)
8. [Ha] Hausdorff F 1918 Dimension und äußeres Maß Mathematische Annalen 79 157-79
9. [Lip] Lipman J 1966 Transcendental numbers Queen's Papers in Pure and Applied Mathematics No 7 Queen's University, Kingston, Ont.
10. [Li] Liu Q 1996 The exact Hausdorff dimension of a branching set Probab. Theory Related Fields 104 515-38
11. [Ma] Mather J 1988 Destruction of invariant circles Ergodic Theory Dynam. Systems 8 199-214
12. [MWW] Ma J-H, Wen Z-Y and Wu J 2002 Besicovitch subsets of self-similar sets Ann. Inst. Fourier 52 1061-74
13. [Ox] Oxtoby J 1980 Measure and Category (Berlin: Springer)
14. [Ro] Rogers C A 1970 Hausdorff Measures (London: Cambridge University Press)
15. [St] Stromberg K 1981 An Introduction to Classical Real Analysis (Belmont, CA: Wadsworth & Brooks)
16. [Yo] Yoccoz J-C 1995 Centralisateurs et conjugaison diffrentiable des diffomorphismes du cercle Astérisque 231 89-242