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Open Access Original Articles

Finer Structure of the Multifractal Spectrum of Local Entropies

pp. 161–175Vol. 6Issue 2June 2013DOI: 10.1080/1726037X.2008.10698554XML
Published Online:
03 Jun 2013
Article type:
Original Articles
Language:
EN
Article no.:
1726037X.2008.10698554
Pages:
161–175

Abstract

We consider a finer decomposition for the multifractal spectrum of local entropies ε (α) =: h (f, K:= {x : h (f, x) = α}). This consists in taking a partition for each multifractal set of the form

Keywords

References

  1. Badii, R., Paladin, G., Parisi, G. and Vulpiani, A.1984 . , 17 : 3521
  2. Badii, R. and Polliti, A.1987 . , 35 : 243
  3. Barreira, L., Pesin, Y. and Schmeling, J.1997 . On a General Concept of Multifractality: Multifractal Spectra for Dimension, Entropies and Lyapunov Exponents . , 7 ( 1 ) : 27
  4. Barreira, L., Saussol, B. and Schmeling, J.2002 . Higher dimensional and multifractal analysis . , 81 : 67 – 91 .
  5. Barreira, L. and Schmeling, J.2000 . Sets of ”non-typical” points have full topological entropy and full Hausdorff dimension . , 116 : 29 – 70 .
  6. Bowen, R.1973 . Topological entropy for non-compact sets . , 184 : 125 – 136 .
  7. Bowen, R. E.1971 . Periodic points and measures for Axiom-A diffeomorphisms . , 154 : 377 – 397 .
  8. Brin, M. and Katok, A.1983 . “ On local entropy in ” . In , Vol. 1007 , Springer . of
  9. Collet, P., Lebowitz, J. and Porzio, A.1987 . , 47 : 609
  10. Denker, M. and Phillip, W.1984 . Apromation by Brownian motions for Gibbs measures and flows under a faunction . , 4 : 541 – 552 .
  11. Ercai, C., Küpper, T. and Lin, S.2005 . Topological entropy for divergence points . , 25 : 1173 – 1208 .
  12. Halsey, T.C., Jensen, M., Kadanoff, L., Procaccia, I. and Shraiman, B.1986 . Fractal Measures and Their Singularities . , 33 : 1141
  13. Hentschel, H. G. E. and Procaccia, I.1983 . The infinite number of generalized dimensions of Fractals and strange attractors . , 8 : 435
  14. Hirayama, M.2005 . Second variational formulae for dimension spectra . , 118 : 103 – 118 .
  15. Katok, A. and Hasselblatt, B.1995 . , Cambridge Univ. Pres .
  16. Jordan, T. and Pollicott, M.2007 . Multifractal analysis and the variance of Gibbs measures . , 76 : 57 – 72 .
  17. Mesón, A. M. and Vericat, F.2004 . variational analysis for the multifractal spectra of local entropies and Lyapunov exponents . , 19 : 1031 – 1038 .
  18. Mesón, A. M. and Vericat, F.2003 . Relations between some quantities in classical thermodynamics and abstract dynamics. Beyond hyperbolicity . , 7 ( 3 ) : 437 – 448 .
  19. Mesón, A. M. and Vericat, F.Simultaneous multifractal decompositions for the spectra of local entropies and ergodic averages . ,
  20. Mesón, A.M. and Vericat, F.2004 . Dimension Theory and Fuchsian groups . , 80 : 95 – 121 .
  21. Mesón, A. M. and Vericat, F.2002 . Geometric constructions and multifractal analysis for boundary hyperbolic maps . , 17 : 203 – 213 .
  22. Olsen, L.2003 . Small sets of divergence points are dimensionless . , 140 : 335 – 350 .
  23. Pesin, Y.1997 . , Chicago and London: The University of Chicago Press .
  24. Pesin, Y. and Zhang, K.2007 . Thermodynamics Associated With Inducing Schemes and Liftability of Measures . , 51 : 289 – 305 .
  25. Ruelle, D.1978 . , Addison-Wesley: Enciclopedia of Mathematics .
  26. Takens, F. and Verbitski, E.1999 . Multifractal Analysis of Local Entropies for Expansive Homeo-morphisms with Specification . , 203 : 593
  27. Takens, F. and Verbitski, E.2000 . On the variational principle for the topological entropy of certain non-compact sets . , 105 : 203 – 237 .
  28. Walters, P.1982 . , Berlin: Springer-Verlag .
  29. Weiss, H.1992 . Some variatinal formulas for Hausdorff dimensions, topological entropy and SRB entropy for hyperbolic dynamical systems . , 69 : 879
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