Fixed point formula for holomorphic functions

Tarkhanov, Nikolai

doi:10.1090/S0002-9939-04-07364-2

Fixed point formula for holomorphic functions
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Proc. Amer. Math. Soc. 132 (2004), 2411-2419 Request permission

Abstract:

We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain $\mathcal {D}$ with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of $\mathcal {D}$, we make use of the Bergman kernel of this domain. The Lefschetz number is proved to be the sum of the usual contributions of fixed points of the map in $\mathcal {D}$ and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points.

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