Publicación:
Generalized fractal dimensions of invariant measures of full-shift systems over compact and perfect spaces: Generic behavior
Generalized fractal dimensions of invariant measures of full-shift systems over compact and perfect spaces: Generic behavior
| dc.contributor.author | Carvalho, Silas L. | es_PE |
| dc.contributor.author | Condori, Alexander | es_PE |
| dc.date.accessioned | 2024-05-30T23:13:38Z | |
| dc.date.available | 2024-05-30T23:13:38Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | In this paper, we show that, for topological dynamical systems with a dense set (in the weak topology) of periodic measures, a typical (in Baire's sense) invariant measure has, for each q>0, zero lower q-generalized fractal dimension. This implies, in particular, that a typical invariant measure has zero upper Hausdorff dimension and zero lower rate of recurrence. Of special interest is the full-shift system (X,T) (where X=Mℤ is endowed with a sub-exponential metric and the alphabet M is a compact and perfect metric space), for which we show that a typical invariant measure has, for each q>1, infinite upper q-correlation dimension. Under the same conditions, we show that a typical invariant measure has, for each s∈(0,1) and each q>1, zero lower s-generalized and infinite upper q-generalized dimensions. © 2021 Walter de Gruyter GmbH, Berlin/Boston 2021. | |
| dc.description.sponsorship | Fondo Nacional de Desarrollo Científico y Tecnológico - Fondecyt | |
| dc.identifier.doi | https://doi.org/10.1515/forum-2020-0023 | |
| dc.identifier.scopus | 2-s2.0-85100073370 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12390/2384 | |
| dc.language.iso | eng | |
| dc.publisher | De Gruyter Open Ltd | |
| dc.relation.ispartof | Forum Mathematicum | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.subject | invariant measures | |
| dc.subject | correlation dimension | es_PE |
| dc.subject | Full-shift over an uncountable alphabet | es_PE |
| dc.subject | generalized fractal dimensions | es_PE |
| dc.subject.ocde | http://purl.org/pe-repo/ocde/ford#2.02.03 | |
| dc.title | Generalized fractal dimensions of invariant measures of full-shift systems over compact and perfect spaces: Generic behavior | |
| dc.type | info:eu-repo/semantics/article | |
| dspace.entity.type | Publication | |
| oairecerif.author.affiliation | #PLACEHOLDER_PARENT_METADATA_VALUE# | |
| oairecerif.author.affiliation | #PLACEHOLDER_PARENT_METADATA_VALUE# |