Abstract
We give a complete description of the stable subset (the union of all backward orbit with bounded step) and of the pre-models of a univalent self-map \(f:X\rightarrow X\), where X is a Kobayashi hyperbolic cocompact complex manifold, such as the ball or the polydisc in \(\mathbb {C}^q\). The result is obtained studying the complex structure of a decreasing intersection of complex manifolds, all biholomorphic to X.
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Supported by the ERC Grant “HEVO - Holomorphic Evolution Equations” No. 277691.
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Arosio, L. The stable subset of a univalent self-map. Math. Z. 281, 1089–1110 (2015). https://doi.org/10.1007/s00209-015-1521-9
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DOI: https://doi.org/10.1007/s00209-015-1521-9