Properties of quasi-Assouad dimension
The connections between quasi-Assouad dimension and tangents are studied. We apply these results to the calculation of the quasi-Assouad dimension for a class of planar selfaffine sets. We also show that sets with decreasing gaps have quasi-Assouad dimension 0 or 1 and exhibit an example of a set in...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/182284 |
| Acceso en línea: | http://hdl.handle.net/11336/182284 |
| Access Level: | acceso abierto |
| Palabra clave: | ASSOUAD DIMENSION ORTHOGONAL PROJECTIONS WEAK TANGENTS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | The connections between quasi-Assouad dimension and tangents are studied. We apply these results to the calculation of the quasi-Assouad dimension for a class of planar selfaffine sets. We also show that sets with decreasing gaps have quasi-Assouad dimension 0 or 1 and exhibit an example of a set in the plane whose quasi-Assouad dimension is smaller than that of its projection onto the x-axis, showing that quasi-Assouad dimension may increase under Lipschitz mappings. Moreover, for closed sets, we show that the Hausdorff dimension is an upper bound for the quasi-lower Assouad dimension |
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