Local dynamics for fibered holomorphic transformations

TL;DR

This paper investigates the local behavior of fibered holomorphic transformations near invariant curves, extending known results from the non-fibered case to this more complex setting.

Contribution

It provides new insights into the dynamics of fibered holomorphic transformations near invariant curves, bridging a gap with classical non-fibered dynamics.

Findings

Results analogous to non-fibered case established

Characterization of local dynamics near invariant curves

Extension of classical dynamics results to fibered setting

Abstract

Fibered holomorphic dynamics are skew-product transformations over an irrational rotation, whose fibers are holomorphic functions. In this paper we study such a dynamics on a neighborhood of an invariant curve. We obtain some results analogous to the results in the non fibered case.