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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.
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[2] |
R. Bowen, Hausdorff dimension of quasi-circles,, IHES Publ., 50 (1979), 259. Google Scholar |
[3] |
G. Birkhoff, "Lattice Theory,", 3rd edition, (1967).
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[4] |
K. Falconer, Dimensions and measures of quasi self-similar sets,, Proc. Amer. Math. Soc., 106 (1989), 543.
doi: 10.1090/S0002-9939-1989-0969315-8. |
[5] |
H. Furstenberg and H. Kesten, Products of random matrices,, Ann. Math. Statist., 31 (1960), 457.
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.
|
[7] |
C. Liverani, Decay of correlations,, Annals Math. (2), 142 (1995), 239.
doi: 10.2307/2118636. |
[8] |
D. Ruelle, Repellers for real analytic maps,, Erg. Th. & Dyn. Syst., 2 (1982), 99.
|
[9] |
D. Ruelle, Differentiation of SRB states,, Comm. Math. Phys., 187 (1997), 227.
doi: 10.1007/s002200050134. |
[10] |
H. H. Rugh, Coupled maps and analytic function spaces,, Ann. Scient. Éc. Norm. Sup. (4), 35 (2002), 489.
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.
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.
|
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.
|
[2] |
R. Bowen, Hausdorff dimension of quasi-circles,, IHES Publ., 50 (1979), 259. Google Scholar |
[3] |
G. Birkhoff, "Lattice Theory,", 3rd edition, (1967).
|
[4] |
K. Falconer, Dimensions and measures of quasi self-similar sets,, Proc. Amer. Math. Soc., 106 (1989), 543.
doi: 10.1090/S0002-9939-1989-0969315-8. |
[5] |
H. Furstenberg and H. Kesten, Products of random matrices,, Ann. Math. Statist., 31 (1960), 457.
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.
|
[7] |
C. Liverani, Decay of correlations,, Annals Math. (2), 142 (1995), 239.
doi: 10.2307/2118636. |
[8] |
D. Ruelle, Repellers for real analytic maps,, Erg. Th. & Dyn. Syst., 2 (1982), 99.
|
[9] |
D. Ruelle, Differentiation of SRB states,, Comm. Math. Phys., 187 (1997), 227.
doi: 10.1007/s002200050134. |
[10] |
H. H. Rugh, Coupled maps and analytic function spaces,, Ann. Scient. Éc. Norm. Sup. (4), 35 (2002), 489.
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.
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.
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