Toronto, 6 - 9 décembre 2019
Based on joint works with D. Beliaev, Y. Han, H. Ho, B. Le, C. Nguyen, M. Zinsmeister.
If time permits, we will discuss and extend to any dimension the general definition of fractality proposed by the author (and M-vF) in , as the presence of nonreal complex dimensions. Finally, we may also discuss fractal tube formulas which enable us to express the intrinsic oscillations of fractal objects in terms of the underlying complex dimensions and the residues of the associated fractal zeta functions. Intuitively, the real parts of the complex dimensions correspond to the amplitudes of the associated “geometric waves”, while their imaginary parts correspond to the frequencies of those waves.