A continuity property of the dimension of the harmonic measure of Cantor sets under perturbations

Athanassios Batakis

Annales de l'I.H.P. Probabilités et statistiques (2000)

  • Volume: 36, Issue: 1, page 87-107
  • ISSN: 0246-0203

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Batakis, Athanassios. "A continuity property of the dimension of the harmonic measure of Cantor sets under perturbations." Annales de l'I.H.P. Probabilités et statistiques 36.1 (2000): 87-107. <http://eudml.org/doc/77651>.

@article{Batakis2000,
author = {Batakis, Athanassios},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {perturbation; convergence; continuity; Hausdorff dimension; Cantor sets; harmonic measures},
language = {eng},
number = {1},
pages = {87-107},
publisher = {Gauthier-Villars},
title = {A continuity property of the dimension of the harmonic measure of Cantor sets under perturbations},
url = {http://eudml.org/doc/77651},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Batakis, Athanassios
TI - A continuity property of the dimension of the harmonic measure of Cantor sets under perturbations
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2000
PB - Gauthier-Villars
VL - 36
IS - 1
SP - 87
EP - 107
LA - eng
KW - perturbation; convergence; continuity; Hausdorff dimension; Cantor sets; harmonic measures
UR - http://eudml.org/doc/77651
ER -

References

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  2. [2] Z. Balogh, I. Popovici and A. Volberg, Conformally maximal polynomial-like dynamics and invariant harmonic measure, Ergodic Theory Dynamical Systems17 (1) (1997) 1-27. Zbl0876.58036MR1440765
  3. [3] A. Batakis, Harmonic measure of some Cantor type sets, Ann. Acad. Sci. Fenn.21 (1996) 255-270. Zbl0849.31005MR1404086
  4. [4] A. Batakis, Théorie du potentiel : 1. Sur les domaines Poissoniens 2. Sur la mesure harmonique des ensembles de Cantor, Ph.D. Thesis, Université de Paris-Sud, 1997. 
  5. [5] A. Batakis and Y. Heurteaux, On relations between entropy and Hausdorff dimension of measures, Preprint, Prépublications d'Orsay, 1998. MR1946341
  6. [6] A. Beardon, On the Hausdorff dimension of general Cantor sets, Proc. Cambridge Philos. Soc.61 (1965) 679-694. Zbl0145.05502MR177083
  7. [7] L. Carleson, On the support of harmonic measure for sets of Cantor type, Ann. Acad. Sci. Fenn.10 (1985) 113-123. Zbl0593.31004MR802473
  8. [8] A.H. Fan, Sur la dimension des mesures, Studia Math.111 (1994) 1-17. Zbl0805.28002
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  10. [10] Y. Heurteaux, Estimations de la dimension inférieure et de la dimension supérieure des mesures, Ann. Inst. H. PoincaréProbab. Statist.34 (1998) 309-338. Zbl0903.28005MR1625871
  11. [11] M. Lyubich and A. Volberg, A comparison of harmonic and balanced measures on Cantor repellors, J. Fourier Analysis and Applications (Special Issue J.-P. Kahane) (1995) 379-399. Zbl0891.58024
  12. [12] N. Makarov and A. Volberg, On the harmonic measure of discontinuous fractals, Preprint LOMI E-6-86, Leningrad, 1986. 
  13. [13] P. Mattila, Geometric Measure Theory, Cambridge University Press, 1995. Zbl0883.28006MR1333890
  14. [14] A. Volberg, On harmonic measure of self-similar sets in the plane, in: Harmonic Analysis and Discrete Potential Theory, Plenum Press, 1992. MR1222465
  15. [15] A. Volberg, On the dimension of harmonic measure of Cantor-type repellers, Michigan Math. J.40 (1993) 239-258. Zbl0797.30022MR1226830
  16. [16] M. Zinsmeister, Formalisme Thermodynamique et Systèmes Dynamiques Holomorphes. Panoramas et Synthèses, Vol. 4, Société Mathématique de France, 1997. Zbl0879.58042MR1462079

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