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Differentiability of fractal curves
A self-similar set that spans [dbl-struck R] super(n) can have no tangent hyperplane at any single point. There are lots of smooth self-affine curves, however. We consider plane self-affine curves without double points and with two pieces. There is an open subset of parameter space for which the cur...
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| Published in: | Nonlinearity 2011-10, Vol.24 (10), p.2717-2728 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c357t-4553b2868990fb7e8fffa45b4e334fc302d33de4b4d9b42257aa61b6eb5275493 |
| container_end_page | 2728 |
| container_issue | 10 |
| container_start_page | 2717 |
| container_title | Nonlinearity |
| container_volume | 24 |
| creator | BANDT, Christoph KRAVCHENKO, Aleksey |
| description | A self-similar set that spans [dbl-struck R] super(n) can have no tangent hyperplane at any single point. There are lots of smooth self-affine curves, however. We consider plane self-affine curves without double points and with two pieces. There is an open subset of parameter space for which the curve is differentiable at all points except for a countable set. For a parameter set of codimension one, the curve is continuously differentiable. However, there are no twice differentiable self-affine curves in the plane, except for line segments and parabolic arcs. |
| doi_str_mv | 10.1088/0951-7715/24/10/003 |
| format | article |
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| fulltext | fulltext |
| identifier | ISSN: 0951-7715 |
| ispartof | Nonlinearity, 2011-10, Vol.24 (10), p.2717-2728 |
| issn | 0951-7715 1361-6544 |
| language | eng |
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| source | Institute of Physics:Jisc Collections:IOP Publishing Read and Publish 2024-2025 (Reading List) |
| subjects | Exact sciences and technology Fractal analysis Fractals Global analysis, analysis on manifolds Hyperplanes Mathematical analysis Mathematical methods in physics Mathematics Measure and integration Nonlinearity Other topics in mathematical methods in physics Physics Planes Sciences and techniques of general use Segments Self-similarity Tangents Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Differentiability of fractal curves |
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