Angular extents and trajectory slopes in the theory of holomorphic\n semigroups in the unit disk

2020/10/05 by Manuel D. Contreras, Contreras, Manuel D., Santiago Díaz‐Madrigal +3
Mathematics · Physics and Astronomy · #30C45 #34M15 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary: 30D05 #Quantum chaos and dynamical systems #Secondary: 30C35

paper · pdf · doi:10.48550/arxiv.2010.01883

openalex publication_date 2020/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study relationships between the asymptotic behaviour of a non-elliptic\nsemigroup of holomorphic self-maps of the unit disk and the geometry of its\nplanar domain (the image of the Koenigs function). We establish a sufficient\ncondition for the trajectories of the semigroup to converge to its Denjoy-Wolff\npoint with a definite slope. We obtain as a corollary two previously known\nsufficient conditions.\n

Related

• Slope problem for trajectories of holomorphic semigroups in the unit disc
• Asymptotic behavior of orbits of holomorphic semigroups
• Non-tangential limits and the slope of trajectories of holomorphic semigroups of the unit disc
• Semigroup-fication of univalent self-maps of the unit disc
• Boundary behavior and rigidity of semigroups of holomorphic mappings