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Generic unfolding of an antiholomorphic parabolic point of codimension k
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems , First View
- Published online by Cambridge University Press:
- 23 October 2025, pp. 1-31
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- Article
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We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension k (i.e. a fixed point of multiplicity
$k+1$) under conjugacy. Such generic unfoldings depend real analytically on k real parameters. A preparation of the unfolding allows to identify real analytic canonical parameters, which are preserved by any conjugacy between two prepared generic unfoldings. A modulus of analytic classification is defined, which is an unfolding of the modulus assigned to the antiholomorphic parabolic point. Since the second iterate of such a germ is a real unfolding of a holomorphic parabolic point, the modulus is a special form of an unfolding of the Écalle–Voronin modulus of the second iterate of the antiholomorphic parabolic germ. We also solve the problem of the existence of an antiholomorphic square root to a germ of a generic analytic unfolding of a holomorphic parabolic germ.
