Multilevel Contours on Bundles of Complex Planes

TL;DR

This paper introduces the concept of multilevel contours on bundles of complex planes, establishing theorems and analyzing their behavior in random environments, with potential applications in understanding complex dynamics.

Contribution

The paper presents a novel concept of multilevel contours on complex plane bundles, along with new theorems and properties, advancing the understanding of complex dynamics and data removal processes.

Findings

Theorems on contours in complex plane bundles are established.

Behavior of multilevel contours in random environments is analyzed.

Properties of contours related to 'islands' and 'holes' are studied.

Abstract

A new concept called multilevel contours is introduced through this article by the author. Theorems on contours constructed on a bundle of complex planes are stated and proved. Multilevel contours can transport information from one complex plane to another. Within a random environment, the behavior of contours and multilevel contours passing through the bundles of complex planes are studied. Further properties of contours by a removal process of the data are studied. The concept of 'islands' and 'holes' within a bundle is introduced through this article. These all constructions help to understand the dynamics of the set of points of the bundle. Further research on the topics introduced here will be followed up by the author. These include closed approximations of the multilevel contour formations and their removal processes. The ideas and results presented in this article are novel.