Open Access
Original Articles
Higher Multifractal Analysis for Simultaneous Actions of Fuchsian Groups
ALEJANDRO MESÓNmeson@iflysib.unlp.edu.arGrupo de Aplicaciones Matemáticas y Estadísticas de la Facultad de Ingeniería (GAMEFI) UNLPInstituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB) CONICET-UNLP-CICPBALa Plata, ArgentinaView full profile → , FERNANDO VERICATvericat@iflysib.unlp.edu.arGrupo de Aplicaciones Matemáticas y Estadísticas de la Facultad de Ingeniería (GAMEFI) UNLPInstituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB) CONICET-UNLP-CICPBALa Plata, ArgentinaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 15 Aug 2007
- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2007.10698532
- Pages:
- 125–140
Abstract
We consider groups Γ1, Γ2, …, Γundefined acting on the hyperbolic plane H2 and by the method of Series for coding hyperbolic geodesics we can do simultaneous multifractal decompositions from the action of these groups. We obtain a variational formula for a dimension of the multifractal sets which generalizes that presented in our previous article for d = 1.
Keywords
References
- 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
- Barreira, L., Saussol, B. and Schmeling, J.2002 . Higher dimensional and multifractal analysis . , 81 : 67 – 91 .
- Brin and Katok, A.1983 . “ On local entropy in ” . In , Vol. 1007 , Springer . of
- Bowen, R. E. and Series, C.1979 . Markov maps associated to Fuchsian groups . , 50 : 153 – 170 .
- Carathéodory, C.1914 . . , : 406 – 426 .
- Katok, A. and Hasselblatt, B.1995 . , Cambridge Univ. Press .
- Mesón, A.M. and Vericat, F.2004 . Dimension Theory and Fuchsian Groups . , 80 : 95 – 121 .
- Pesin, Y.1997 . , Chicago and London: The University of Chicago Press .
- Ruelle, D.1978 . , Addison-Wesley: Enciclopedia of Mathematics .
- Series, C.1991 . , Edited by: Bedford, T., Keane, M. and Series, C.Oxford: Oxford University Press . in
- Series, C.1986 . Geoemtrical Markov coding on surfaces of constant negative curvature . , 6
- Takens, F. and Verbitski, E.1999 . Multifractal analysis of local entropies for expansive homeomorphisms with specifications . , 203 : 593 – 612 .
- Takens, F. and Verbitski, E.2003 . On the variational principle for the topological entropy of certain non-compact set . , 23 : 317 – 348 .
- Walters, P.1982 . , Berlin: Springer-Verlag .
Views: 44Downloads: 82Citations: 0
