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Volumn 7, Issue 4, 2001, Pages 535-551

Multifractal analysis of ergodic averages: A generalization of eggleston's theorem

Author keywords

[No Author keywords available]

Indexed keywords

FRACTALS; INTEGRAL EQUATIONS; MARKOV PROCESSES; NONLINEAR EQUATIONS; PROBABILITY DISTRIBUTIONS; THEOREM PROVING; TOPOLOGY;

EID: 0035497207     PISSN: 10792724     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1013158601371     Document Type: Article
Times cited : (13)

References (25)
  • 2
    • 0001235413 scopus 로고
    • The description of a random field by means of conditional probabilities and conditions of its regularity
    • R. L. Dobrushin, The description of a random field by means of conditional probabilities and conditions of its regularity. Theory Probab. Appl. 13 (1968), 197-224.
    • (1968) Theory Probab. Appl. , vol.13 , pp. 197-224
    • Dobrushin, R.L.1
  • 3
    • 0002672692 scopus 로고
    • The fractional dimension of a set defined by decimal properties
    • H. G. Eggleston, The fractional dimension of a set defined by decimal properties. Quart. J. Math. Oxford Ser. 20 (1949), 31-36.
    • (1949) Quart. J. Math. Oxford Ser. , vol.20 , pp. 31-36
    • Eggleston, H.G.1
  • 6
    • 0033453701 scopus 로고    scopus 로고
    • Hausdorff dimension and thermodynamic formalism
    • B. Gurevich and A. Tempelman, Hausdorff dimension and thermodynamic formalism. Russian Math. Surveys 54 (1999), No. 2, 171-172.
    • (1999) Russian Math. Surveys , vol.54 , Issue.2 , pp. 171-172
    • Gurevich, B.1    Tempelman, A.2
  • 9
    • 0001453764 scopus 로고
    • A generalized Shannon-McMillan theorem for the action of an amenable group on a probability space
    • J. C. Kieffer, A generalized Shannon-McMillan theorem for the action of an amenable group on a probability space. Ann. Probab. 3 (1975), No. 6, 1031-1037.
    • (1975) Ann. Probab. , vol.3 , Issue.6 , pp. 1031-1037
    • Kieffer, J.C.1
  • 10
    • 0000799233 scopus 로고
    • Observables at infinite and states with short range correlation in statistical mechanics
    • O. E. Lanford and D. Ruelle, Observables at infinite and states with short range correlation in statistical mechanics. Comm. Math. Phys. 13 (1969), 194-215.
    • (1969) Comm. Math. Phys. , vol.13 , pp. 194-215
    • Lanford, O.E.1    Ruelle, D.2
  • 11
    • 0039771567 scopus 로고
    • Additive functions of intervals and Hausdorff dimension
    • P. Moran, Additive functions of intervals and Hausdorff dimension. Proc. Camb. Phil. Soc. 42 (1946), 15-23.
    • (1946) Proc. Camb. Phil. Soc. , vol.42 , pp. 15-23
    • Moran, P.1
  • 12
    • 0033229030 scopus 로고    scopus 로고
    • Multifractal analysis in symbolic dynamics and distribution of pointwise dimension for g-measures
    • E. Olivier, Multifractal analysis in symbolic dynamics and distribution of pointwise dimension for g-measures. Nonlinearity 12 (1999), No. 6, 1571-1585.
    • (1999) Nonlinearity , vol.12 , Issue.6 , pp. 1571-1585
    • Olivier, E.1
  • 13
    • 51249179168 scopus 로고
    • Entropy and isomorphism theorems for actions of amenable groups
    • D. S. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups. J. Anal. Math. 48 (1987), 1-141.
    • (1987) J. Anal. Math. , vol.48 , pp. 1-141
    • Ornstein, D.S.1    Weiss, B.2
  • 15
    • 0030353353 scopus 로고    scopus 로고
    • On the dimension of deterministic and random Cantor-like sets, symbolic dynamics, and Eckmann-Ruelle conjecture
    • Ya. Pesin and H. Weiss, On the dimension of deterministic and random Cantor-like sets, symbolic dynamics, and Eckmann-Ruelle conjecture. Comm. Math. Phys. 182 (1996), 105-153.
    • (1996) Comm. Math. Phys. , vol.182 , pp. 105-153
    • Pesin, Ya.1    Weiss, H.2
  • 16
    • 0011777599 scopus 로고    scopus 로고
    • The multifractal analysis of Birkhoff averages and large deviations
    • Festschrift dedicated to Floris Takens for his 60th birthday (to appear)
    • _, The multifractal analysis of Birkhoff averages and large deviations. In: Global analysis of dynamical systems, Festschrift dedicated to Floris Takens for his 60th birthday (2001) (to appear).
    • (2001) Global Analysis of Dynamical Systems
  • 18
    • 0004267646 scopus 로고
    • Princeton Univ. Press, Princeton, NJ
    • T. Rockafellar, Convex analysis. Princeton Univ. Press, Princeton, NJ, 1970.
    • (1970) Convex Analysis
    • Rockafellar, T.1
  • 19
    • 0033242957 scopus 로고    scopus 로고
    • Multifractal analysis of local entropies for expansive homeomorphisms with specification
    • F. Takens and E. Verbitski, Multifractal analysis of local entropies for expansive homeomorphisms with specification. Comm. Math. Phys. 203 (1999), No. 3, 593-612.
    • (1999) Comm. Math. Phys. , vol.203 , Issue.3 , pp. 593-612
    • Takens, F.1    Verbitski, E.2
  • 21
    • 0000184355 scopus 로고
    • Ergodic theorems for general dynamical systems
    • A. A. Tempelman, Ergodic theorems for general dynamical systems. Sov. Math. Dokl. 8 (1967), 1213-1216.
    • (1967) Sov. Math. Dokl. , vol.8 , pp. 1213-1216
    • Tempelman, A.A.1
  • 22
    • 0002613757 scopus 로고
    • Ergodic theorems for general dynamical systems
    • _, Ergodic theorems for general dynamical systems. Proc. Moscow Math. Soc. 26 (1972), 94-132.
    • (1972) Proc. Moscow Math. Soc. , vol.26 , pp. 94-132
  • 23
    • 0011743564 scopus 로고
    • Specific characteristics and variational principle for homogeneous random fields
    • _, Specific characteristics and variational principle for homogeneous random fields. Z. Wahrscheinlichkeitstheory und verw. Gebiete 65 (1984), 341-365.
    • (1984) Z. Wahrscheinlichkeitstheory und Verw. Gebiete , vol.65 , pp. 341-365
  • 25
    • 0033622290 scopus 로고    scopus 로고
    • Dimension of random fractals in metric spaces
    • _, Dimension of random fractals in metric spaces. Theory Probab. Appl. 44 (1999), No. 3, 589-616.
    • (1999) Theory Probab. Appl. , vol.44 , Issue.3 , pp. 589-616


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.