Existence of attracting invariant 2-curves in fibred quadratic dynamics

TL;DR

This paper constructs new invariant multi-curves in fibred quadratic dynamics over irrational rotations and extends the local dynamical theory for attracting invariant curves to these objects.

Contribution

It introduces the concept of multi-curves as new invariant sets and extends the local dynamical theory to include these structures.

Findings

Existence of attracting invariant multi-curves in fibred quadratic systems.

Extension of local dynamical theory to multi-curves.

New methods for constructing invariant sets in fibred dynamics.

Abstract

We present a construction of new invariant sets for fibred polynomial dynamics with base an irrational rotation over the unit circle, called multi-curves. Furthermore, the local dynamical theory for attracting invariant curves is extended to these objects.