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• W3093449145 abstract "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 to the generalized asymptotic expansion of the tube function of orbits with oscillatory coefficients as well as to the asymptotic expansion of their dynamically regularized tube function. Interestingly, parabolic orbits provide a first example of sets that have nontrivial Minkowski (or box) dimension and their tube function possesses higher order oscillatory terms, however, they do not posses non-real complex dimensions and are therefore not called fractal in the sense of Lapidus." @default.
• W3093449145 created "2020-10-22" @default.
• W3093449145 creator A5021360613 @default.
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• W3093449145 date "2022-08-29" @default.
• W3093449145 modified "2023-10-10" @default.
• W3093449145 title "Fractal zeta functions of orbits of parabolic diffeomorphisms" @default.
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• W3093449145 doi "https://doi.org/10.1007/s13324-022-00724-3" @default.
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