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Box dimension and Minkowski content of generalized Euler spirals

We show that the box dimension of the generalized Euler spirals generated by control functions with $p$-growth at infinity is equal to the box dimension of the $p$-clothoid, $p>1$, also called the generalized Euler or Cornu spiral. This dimension is equal to $d=2p/(2p-1)$. Furthermore, this curve is Minkowski measurable, and we compute its $d$-dimensional Minkowski content. We provide a new, elementary and simple proof of the asymptotic expansion of generalized Fresnel integrals generated by control functions with $p$-growth at infinity. This work is made in collaboration with Luka Korkut, Darko \v Zubrini\' c and Vesna \v Zupanovi\'c. Poster presented by Domagoj Vlah.

Generalized Euler or Cornu spiral; box dimension; Minkowski content; generalized Fresnel integrals

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