# Fractal zeta functions of orbits of parabolic diffeomorphisms

@article{Mardei2020FractalZF, title={Fractal zeta functions of orbits of parabolic diffeomorphisms}, author={P. Marde{\vs}i{\'c} and Goran Radunovi'c and Maja Resman}, journal={Analysis and Mathematical Physics}, year={2020}, volume={12} }

In this paper, we prove that fractal zeta functions of orbits of parabolic germs of diffeomorphisms can be meromorphically extended to the whole complex plane. We describe their set of poles (i.e. their complex dimensions) and their principal parts which can be understood as their fractal footprint. We study the fractal footprint of one orbit of a parabolic germ f and extract intrinsic information about the germ f from it, in particular, its formal class. Moreover, we relate complex dimensions…

## One Citation

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