Naishul's Theorem for fibred holomorphic maps

TL;DR

This paper proves that the fibred rotation number, linked to an indifferent invariant curve, remains unchanged under topological conjugacies for fibred holomorphic maps, highlighting its role as a topological invariant.

Contribution

It establishes that the fibred rotation number is a topological invariant for indifferent invariant curves in fibred holomorphic maps, extending understanding of their topological properties.

Findings

Fibred rotation number is a topological invariant.

Indifferent invariant curves have rotation numbers preserved under topological conjugacy.

The result applies specifically to fibred holomorphic maps.

Abstract

We show that the fibred rotation number associated to an indifferent invariant curve for a fibred holomorphic map is a topological invariant.