UKURAN KURVATUR FRAKTAL PADA HIMPUNAN SERUPA DIRI
| Main Authors: | , Ari Puji Prasetiyo, , Prof. Dr.rer.nat. Widodo, MS. |
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| Format: | Thesis NonPeerReviewed |
| Terbitan: |
[Yogyakarta] : Universitas Gadjah Mada
, 2013
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| Subjects: | |
| Online Access: |
https://repository.ugm.ac.id/123178/ http://etd.ugm.ac.id/index.php?mod=penelitian_detail&sub=PenelitianDetail&act=view&typ=html&buku_id=63289 |
Daftar Isi:
- Curvature measures are an important tool in geometric measure theory and other fields of mathematics for describing the geometry of sets in Euclidean space. But the �classical� concepts of curvature are not directly applicable to fractal sets. In order to bridge this gap between geometric measure theory and fractal geometry by introducing a notion of curvature for fractals. For compact sets (e.g. fractals), for which classical geometric characteristic such as curvatures is not available, this notions for their �parallel sets * ( ) + are studied instead, expecting that their limiting behaviour as does provide information about the structure of the initial set . In particular, the limiting behaviour of the total curvatures (or intrinsic volumes) ( ), , are investigated as well as weak limits of the corresponding curvature measures ( ) as . This leads to the notions of fractal curvature and fractal curvature measure, respectively. The well�known Minkowski content appears in this concept as one of the fractal curvatures. For certain classes of self�similar sets, results on the existence of (averaged) fractal curvatures are presented. These limits can be calculated explicitly and are in a certain sense �invariants� of the sets, which may help to distinguish and classify fractals. Based on these results also the fractal curvature measures of these sets are characterized.