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- W3088252502 abstract "We address the inverse problem for holomorphic germs of a tangent-to-identity mapping of the complex line near a fixed point. We provide a preferred (family of) parabolic map $Delta$ realizing a given Birkhoff–Ecalle-Voronin modulus $psi$ and prove its uniqueness in the functional class we introduce. The germ is the time-1 map of a Gevrey formal vector field admitting meromorphic sums on a pair of infinite sectors covering the Riemann sphere. For that reason, the analytic continuation of $Delta$ is a multivalued map admitting finitely many branch points with finite monodromy. In particular $Delta$ is holomorphic and injective on an open slit sphere containing 0 (the initial fixed point) and $infty$, where sits the companion parabolic point under the involution $frac{-1}{id}$. It turns out that the Birkhoff–Ecalle-Voronin modulus of the parabolic germ at $infty$ is the inverse $psi^{circ-1}$ of that at 0." @default.
- W3088252502 created "2020-10-01" @default.
- W3088252502 creator A5077024768 @default.
- W3088252502 date "2020-09-23" @default.
- W3088252502 modified "2023-10-16" @default.
- W3088252502 title "Spherical normal forms for germs of parabolic line biholomorphisms" @default.
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