Naslov
Fractal dimensions of oscillatory integrals

Autori
Rolin, Jean-Philippe ; Vlah, Domagoj ; Županović, Vesna

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications

Mjesto i datum
Madrid, Španjolska, 07.07.2014. - 11.07.2014

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
singularity theory; oscillatory integrals; Fresnel integrals; box dimension

Sažetak
It is known that the asymptotics of oscillatory integrals has been related to singularities of the phase function. Abelian integrals and Fresnel integrals are well known classes of oscillatory integrals. Motivated by geometrical interpretation of Fresnel integrals by a spiral called the clothoid, we continue investigation concerning geometrical approach to oscillatory integrals. Using the point of view of fractal geometry, we consider oscillatory integrals depending on one parameter $t$. Oscillatority is measured by the box dimension of the plane curve parameterized by $x(t)$ and $y(t)$ that are the real and imaginary part of the integral, respectively. Also, the oscillatory dimension is defined as the box dimension of the graph $X(\tau) = x(1/\tau)$, near $\tau=0$, where $x(t)$ for $t>0$ is the graph of the real part of the integral. Analogously for $y(t)$ and the imaginary part of the integral. We investigate the connection between these dimensions and asymptotics of the integral.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA