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On dimensions of conformal repellers. Randomness and parameter dependency
| 1. | Department of Mathematics, University of Paris Sud 11, F-91405 Orsay, France |
References:
| [1] |
L. M. Barreira, A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems, Erg. Th. & Dyn. Syst., 16 (1996), 871-927. |
| [2] |
R. Bowen, Hausdorff dimension of quasi-circles, IHES Publ., 50 (1979), 259-273. |
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G. Birkhoff, "Lattice Theory," 3rd edition, American Mathematical Society Colloquium Publications, Vol. XXV, Amer. Math. Soc., Providence, RI, 1967. |
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K. Falconer, Dimensions and measures of quasi self-similar sets, Proc. Amer. Math. Soc., 106 (1989), 543-554.
doi: 10.1090/S0002-9939-1989-0969315-8. |
| [5] |
H. Furstenberg and H. Kesten, Products of random matrices, Ann. Math. Statist., 31 (1960), 457-469.
doi: 10.1214/aoms/1177705909. |
| [6] |
D. Gatzouras and Y. Peres, Invariant measures of full dimension for some expanding maps, Erg. Th. & Dyn. Syst., 17 (1997), 147-167. |
| [7] |
C. Liverani, Decay of correlations, Annals Math. (2), 142 (1995), 239-301.
doi: 10.2307/2118636. |
| [8] |
D. Ruelle, Repellers for real analytic maps, Erg. Th. & Dyn. Syst., 2 (1982), 99-107. |
| [9] |
D. Ruelle, Differentiation of SRB states, Comm. Math. Phys., 187 (1997), 227-241.
doi: 10.1007/s002200050134. |
| [10] |
H. H. Rugh, Coupled maps and analytic function spaces, Ann. Scient. Éc. Norm. Sup. (4), 35 (2002), 489-535.
doi: 10.1016/S0012-9593(02)01102-3. |
| [11] |
H. H. Rugh, On the dimensions of conformal repellers. Randomness and parameter dependency, Ann. Math. (2), 168 (2008), 695-748.
doi: 10.4007/annals.2008.168.695. |
| [12] |
M. Urbański and A. Zdunik, Real analyticity of Hausdorff dimension of finer Julia sets of exponential family, Erg. Th. & Dyn. Syst., 24 (2004), 279-315. |
show all references
References:
| [1] |
L. M. Barreira, A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems, Erg. Th. & Dyn. Syst., 16 (1996), 871-927. |
| [2] |
R. Bowen, Hausdorff dimension of quasi-circles, IHES Publ., 50 (1979), 259-273. |
| [3] |
G. Birkhoff, "Lattice Theory," 3rd edition, American Mathematical Society Colloquium Publications, Vol. XXV, Amer. Math. Soc., Providence, RI, 1967. |
| [4] |
K. Falconer, Dimensions and measures of quasi self-similar sets, Proc. Amer. Math. Soc., 106 (1989), 543-554.
doi: 10.1090/S0002-9939-1989-0969315-8. |
| [5] |
H. Furstenberg and H. Kesten, Products of random matrices, Ann. Math. Statist., 31 (1960), 457-469.
doi: 10.1214/aoms/1177705909. |
| [6] |
D. Gatzouras and Y. Peres, Invariant measures of full dimension for some expanding maps, Erg. Th. & Dyn. Syst., 17 (1997), 147-167. |
| [7] |
C. Liverani, Decay of correlations, Annals Math. (2), 142 (1995), 239-301.
doi: 10.2307/2118636. |
| [8] |
D. Ruelle, Repellers for real analytic maps, Erg. Th. & Dyn. Syst., 2 (1982), 99-107. |
| [9] |
D. Ruelle, Differentiation of SRB states, Comm. Math. Phys., 187 (1997), 227-241.
doi: 10.1007/s002200050134. |
| [10] |
H. H. Rugh, Coupled maps and analytic function spaces, Ann. Scient. Éc. Norm. Sup. (4), 35 (2002), 489-535.
doi: 10.1016/S0012-9593(02)01102-3. |
| [11] |
H. H. Rugh, On the dimensions of conformal repellers. Randomness and parameter dependency, Ann. Math. (2), 168 (2008), 695-748.
doi: 10.4007/annals.2008.168.695. |
| [12] |
M. Urbański and A. Zdunik, Real analyticity of Hausdorff dimension of finer Julia sets of exponential family, Erg. Th. & Dyn. Syst., 24 (2004), 279-315. |
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