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Invariance of the normalized Minkowski content with respect to the ambient space

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  • Resman, Maja

Abstract

It is easy to show that the lower and the upper box dimensions of a bounded set in Euclidean space are invariant with respect to the ambient space. In this article we show that the Minkowski content of a Minkowski measurable set is also invariant with respect to the ambient space when normalized by an appropriate constant. In other words, the value of the normalized Minkowski content of a bounded, Minkowski measurable set is intrinsic to the set.

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  • Resman, Maja, 2013. "Invariance of the normalized Minkowski content with respect to the ambient space," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 123-128.
    • Handle: RePEc:eee:chsofr:v:57:y:2013:i:c:p:123-128
    DOI: 10.1016/j.chaos.2013.10.001
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    References listed on IDEAS

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    1. Elezović, Neven & Županović, Vesna & Žubrinić, Darko, 2007. "Box dimension of trajectories of some discrete dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 244-252.
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    Cited by:

    1. Miličić, Siniša, 2018. "Box-counting dimensions of generalised fractal nests," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 125-134.
    2. Huzak, Renato & Vlah, Domagoj & Žubrinić, Darko & Županović, Vesna, 2023. "Fractal analysis of degenerate spiral trajectories of a class of ordinary differential equations," Applied Mathematics and Computation, Elsevier, vol. 438(C).

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    1. Huzak, Renato & Vlah, Domagoj & Žubrinić, Darko & Županović, Vesna, 2023. "Fractal analysis of degenerate spiral trajectories of a class of ordinary differential equations," Applied Mathematics and Computation, Elsevier, vol. 438(C).

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