On generalized embeddability of a non-elliptic self-map
Abstract
We study the structure of the centralizer of a non-elliptic holomorphic self-map of the unit disc and its relation with continuous dynamical structures. We prove that if the identity is not isolated in the centralizer of a non-elliptic self-map φ∈ Hol(𝔻), then φ is univalent and its centralizer contains a non-trivial continuous one-parameter semigroup of holomorphic self-maps. This result provides a general criterion for the existence of continuous dynamics arising from discrete iteration. Our approach is based on the theory of holomorphic models and on simultaneous linearization techniques for commuting self-maps. In particular, we exploit recent developments on simultaneous linearization for parabolic self-maps with positive hyperbolic step. As a consequence, we obtain new sufficient conditions for the embeddability of holomorphic self-maps into continuous semigroups.
Related
- Efficient and Accurate Lift-and-Decoupling Generalized Transferable Neural Networks for Elliptic and Moving Interface Problems
- Painlevé Integrability, Hamiltonian Structure and Exact Elliptic Reductions of a Generalized Nonlinear Wave Equation
- Exact Elliptic and Solitary Waves in a Fourth-Order Generalized Burgers–Huxley-Type Equation with Truncated M-Fractional Derivatives
- Generalized Quasi-Symmetric Nets: A Constructive Approach to the Equimodular Elliptic Type and to Flexible m × n Nets
- Non-Elliptic Quadratic 𝒫𝒯-Symmetric Operators and Similarity to Self-Adjoint Operators
BibTeX
@misc{contreras2026generalized,
title = {{On generalized embeddability of a non-elliptic self-map}},
author = {Manuel D. Contreras and Santiago D\'ıaz-Madrigal and Pavel Gumenyuk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19225},
eprint = {2610.19225},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19225},
}
RIS
TY - UNPB
TI - On generalized embeddability of a non-elliptic self-map
AU - Manuel D. Contreras
AU - Santiago D\'ıaz-Madrigal
AU - Pavel Gumenyuk
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.19225
UR - https://arxiv.org/abs/2610.19225
AB - We study the structure of the centralizer of a non-elliptic holomorphic self-map of the unit disc and its relation with continuous dynamical structures. We prove that if the identity is not isolated in the centralizer of a non-elliptic self-map φ∈ Hol(𝔻), then φ is univalent and its centralizer contains a non-trivial continuous one-parameter semigroup of holomorphic self-maps. This result provides a general criterion for the existence of continuous dynamics arising from discrete iteration. Our approach is based on the theory of holomorphic models and on simultaneous linearization techniques for commuting self-maps. In particular, we exploit recent developments on simultaneous linearization for parabolic self-maps with positive hyperbolic step. As a consequence, we obtain new sufficient conditions for the embeddability of holomorphic self-maps into continuous semigroups.
ER -