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Improving dimension estimates for Furstenberg-type sets
- Source :
- idUS. Depósito de Investigación de la Universidad de Sevilla, instname, Adv. Math. 2010;223(2):672-688, Biblioteca Digital (UBA-FCEN), Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales, instacron:UBA-FCEN, CONICET Digital (CONICET), Consejo Nacional de Investigaciones Científicas y Técnicas, instacron:CONICET
- Publication Year :
- 2010
- Publisher :
- Elsevier, 2010.
-
Abstract
- In this paper we prove some lower bounds on the Hausdorff dimension of sets of Furstenberg type. Moreover, we extend these results to sets of generalized Furstenberg type, associated to doubling dimension functions. With some additional growth conditions on the dimension function, we obtain a lower bound on the dimension of "zero dimensional" Furstenberg sets.<br />16 pages, 3 figures
- Subjects :
- Mathematics(all)
Mathematics::Dynamical Systems
28A78, 28A80
Matemáticas
General Mathematics
Furstenberg sets
Mathematics::General Topology
Hausdorff dimension
Matemática Pura
purl.org/becyt/ford/1 [https]
Combinatorics
Dimension function
Classical Analysis and ODEs (math.CA)
FOS: Mathematics
Mathematics - Combinatorics
Hausdorff measure
Mathematics
Mathematical analysis
purl.org/becyt/ford/1.1 [https]
Minkowski–Bouligand dimension
Effective dimension
Packing dimension
Mathematics - Classical Analysis and ODEs
Dimension theory
Combinatorics (math.CO)
Inductive dimension
CIENCIAS NATURALES Y EXACTAS
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- idUS. Depósito de Investigación de la Universidad de Sevilla, instname, Adv. Math. 2010;223(2):672-688, Biblioteca Digital (UBA-FCEN), Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales, instacron:UBA-FCEN, CONICET Digital (CONICET), Consejo Nacional de Investigaciones Científicas y Técnicas, instacron:CONICET
- Accession number :
- edsair.doi.dedup.....bfcc4d33cd96d0a3bf64c25a02227f40