# 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}
}
• Published 12 October 2020
• Mathematics
• Analysis and Mathematical Physics
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…
1 Citations
• Mathematics
• 2021
. In this paper we study germs of diﬀeomorphisms in the complex plane. We address the following problem: How to read a diﬀeomorphism f knowing one of its orbits A ? We solve this problem for

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