Reference : Pointwise regularity of parameterized affine zipper fractal curves fractal curves |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/34159 | |||

Pointwise regularity of parameterized affine zipper fractal curves fractal curves | |

English | |

Bárány, Balázs [Budapest University of Technology and Economy > Stochastic department] | |

Kiss, Gergely [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Kolossváry, István [Alfréd Rényi Institute of Mathematics] | |

Mar-2018 | |

Nonlinearity | |

Institute of Physics | |

31 | |

5 | |

Yes (verified by ORBi^{lu}) | |

International | |

0951-7715 | |

[en] affine zippers ; pointwise Hölder exponent ; multifractal analysis ; pressure function ; iterated function system ; de Rham curve | |

[en] We study the pointwise regularity of zipper fractal curves generated
by affine mappings. Under the assumption of dominated splitting of index-1, we calculate the Hausdorff dimension of the level sets of the pointwise Hölder exponent for a subinterval of the spectrum. We give an equivalent characterization for the existence of regular pointwise Hölder exponent for Lebesgue almost every point. In this case, we extend the multifractal analysis to the full spectrum. In particular, we apply our results for de Rham’s curve. | |

F1R-MTH-PUL-15MRO3 | |

http://hdl.handle.net/10993/34159 | |

10.1088/1361-6544 |

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