Pacific Journal of Mathematics

Conformal repellors with dimension one are Jordan curves.

R. Daniel Mauldin and M. Urbański

Article information

Source
Pacific J. Math., Volume 166, Number 1 (1994), 85-97.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102621246

Mathematical Reviews number (MathSciNet)
MR1306035

Zentralblatt MATH identifier
0865.54037

Subjects
Primary: 58F12
Secondary: 28C99: None of the above, but in this section

Citation

Mauldin, R. Daniel; Urbański, M. Conformal repellors with dimension one are Jordan curves. Pacific J. Math. 166 (1994), no. 1, 85--97. https://projecteuclid.org/euclid.pjm/1102621246


Export citation

References

  • [B] R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomor- phism, L.N.Math., 470, Berlin-Heidelberg-New York, Springer-Verlag, 1975.
  • [EH] S. Eilenberg and O. G. Harrold, Jr., Continua of Finite Linear Measure, Amer. J. Math., 65 (1943), 137-146.
  • [F] K. Falconer, The geometry of fractal sets, Cambridge University Press, 1986.
  • [Kl] K. Kuratowski, Topology, Volume //Academic Press, New York, 1968.
  • [M] K. Menger, Kurventheorie, Chelsea, New York, 1967.
  • [P] F. Przytycki, On holomorphic perturbations of z -- zn, Bull. Polish Acad. Sci. Math., 24 (1986), 127-132.
  • [PUZ] F. Przytycki, M. Urbaski, and A. Zdunik, harmonic, Gibbs and Haus- dorff measures on repellors for holomorphic maps, I, Ann. Math., 130 (1988), 1-40.
  • [Rl] D. Ruelle, Repellors for real analytic maps, Ergodic theory and Dyn. Sys., 2 (1982), 99-107.
  • [R2] D. Ruelle, Bowen's formula for the Hausdorff dimension of self-similar sets in: Scaling and self-similarity in physics-renormalization in statistical mechanics and dynamics, Progress in Physics 7, Birkhauser, Basel, 1983, 351-358.
  • [S] D. Sullivan, Seminar on conformal and hyperbolic geometry by D. P. Sul- livan (notes by M. Baker and J. Seade), preprint IHES (1982).
  • [U] M. Urbanski, On the Hausdorff dimension of a Julia set with a rationally indifferent periodic point, Studia Math., 97 (1991), 167-188.
  • [Whl] G. T. Whyburn, Concerning continua or finite degree and local separating points, Amer. J. Math., 57 (1935), 11-18.
  • [Wh2] G. T. Whyburn, Analytic topology, Amer. Math. Soc. Coll. Publ., 28, Amer. Math. Soc, Providence, R.I., 1942.
  • [W] R. Williams, The structure of Lorenz attractors, Publ. IHES, 50 (1979), 73-99.
  • [Zl] A. Zdunik, Parabolic orbifolds and the dimension of the maximal measure for rational maps, Ivent. Math., 99 (1990), 627-649.
  • [Z2] A. Zdunik, Harmonic measure versus Hausdorff measures on repellors