PreprintarXiv licencearXiv
Dynamics inside the attracting basins of some skew products
Abstract
Polynomial skew products in ℂ2 are maps of the form F(z,w)=(P(z),Q(z,w)), where P and Q are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.
Related
- Fatou Components of Attracting Skew Products: From Polynomial Classification to Transcendental Complexity
- Some Properties of Products of Linear Fractional Composition Operators on Weighted Dirichlet Spaces
- When vector abundance constrains vector-borne transmission: inside epidemic dynamics within a prescribed population
- A note on the non-wandering dynamics in the n-fold symmetric products
- On the Existence of Geometrically Attracting Measures for Iterated Function Systems with Varying Sets of Transformations
BibTeX
@misc{fornæss2026dynamics,
title = {{Dynamics inside the attracting basins of some skew products}},
author = {John Erik Fornæss and Mi Hu and Feng Rong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11075},
eprint = {2609.11075},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11075},
}
RIS
TY - UNPB
TI - Dynamics inside the attracting basins of some skew products
AU - John Erik Fornæss
AU - Mi Hu
AU - Feng Rong
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11075
UR - https://arxiv.org/abs/2609.11075
AB - Polynomial skew products in ℂ^2 are maps of the form F(z,w)=(P(z),Q(z,w)), where P and Q are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.
ER -