Canonical Models on Strongly Convex Domains via the Squeezing Function
Copyright policy )Canonical Models on Strongly Convex Domains via the Squeezing Function
We prove that if a holomorphic self-map $f\colon ��\to ��$ of a bounded strongly convex domain $��\subset \mathbb C^q$ with smooth boundary is hyperbolic then it admits a natural semi-conjugacy with a hyperbolic automorphism of a possibly lower dimensional ball $\mathbb B^k$. We also obtain the dual result for a holomorphic self-map $f\colon ��\to ��$ with a boundary repelling fixed point. Both results are obtained by rescaling the dynamics of $f$ via the squeezing function.
- University of Bari Aldo Moro Italy
- University of Amsterdam Netherlands
- UNIVERSITEIT VAN AMSTERDAM Netherlands
- University of Rome Tor Vergata Italy
Strongly convex domains, Settore MAT/03 - GEOMETRIA, squeezing function, Mathematics - Complex Variables, FOS: Mathematics, canonical models, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Complex Variables (math.CV), iteration theory, 510, 004, 32H50
Strongly convex domains, Settore MAT/03 - GEOMETRIA, squeezing function, Mathematics - Complex Variables, FOS: Mathematics, canonical models, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Complex Variables (math.CV), iteration theory, 510, 004, 32H50
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