Seminar za dinamičke sustave
lokacija:
PMF Matematički odsjek (virtualno)
vrijeme:
26.01.2021 - 16:15 - 18:00 On Tuesday, 26/01/2021, at 16.15,
Goran Radunović, PMF-MO, will give a talk in Dynamical Systems Seminar in Zagreb under the title:
Fractional integro-derivative of fractal zeta functions and Log-Minkowski measurability
Abstract: We introduce Logarithmic gauge Minkowski content which arises
naturally from the theory of complex dimensions. The complex dimensions
of a given set are usually defined as poles of the corresponding fractal
zeta function and they generalize the notion of Minkowski dimension. In
the most simple case the fractal zeta function has a simple pole at D
where D is the Minkowski dimension of the given set, whereas the residue
equals to the Minkowski content (modulo a multiplicative constant).
naturally from the theory of complex dimensions. The complex dimensions
of a given set are usually defined as poles of the corresponding fractal
zeta function and they generalize the notion of Minkowski dimension. In
the most simple case the fractal zeta function has a simple pole at D
where D is the Minkowski dimension of the given set, whereas the residue
equals to the Minkowski content (modulo a multiplicative constant).
Here we show that in case of poles of higher order one has to introduce
a generalization of Minkowski content to obtain an analogue connection.
Furthermore, in the most general case, one has to consider more
complicated singularities of the fractal zeta function, including a
combination of poles, zeroes and branch points. The general case can be
explained in the context of an appropriate fractional integro-derivative
of the fractal zeta function.
The talk will be held via Zoom platform:
Everybody is invited.
Maja Resman
