Inconvenient Delays

So here we are a month since I last posted. I would explain but that would feel like giving excuses and I'm trying to get out of the habit of feeling guilty for things which were out of my hands. I do however have something for you to read and perhaps enjoy.

My most recent deadline has been for a draft masters thesis for my project. This is available for you to read via this link.

What I have written covers about a third of the area of work I have been doing. It is very minimalist and basic with very little of the style or continuity that I duly put in my work. My introduction and background are perhaps not as full as I would like but maybe you can provide some thoughts on that since it is aimed at bringing people of different ranges of knowledge on the subject up to speed before I share my analysis. If there is any point of logic missing please do let me know.

The version I am sharing is the version I would have like to share with the examiners but my supervisor had other ideas so I actually submitted a stripped down version that is even worse so I will not be sharing that.

One point which you should all love is all the images generated that I have included in the report. In my time I have analysed the Julia set changes, the stability changes, the manifolds and most recently the full bifurcations in one half with the other half due to be completed this week. I have finally reached the crux of my examination of the map which is a strange one. The circle hole in one half has an important bearing on the location of the attractor which "disappears" and yet still points remain in the set - this is only possible with an attractor still present yet at some point there doesn't even exist a higher period attractor, just saddles and repellors. Thus this week my question to answer is whether an attractor still appears to exist for the points under the mapping despite the properties attributed to it or if the boundary of the hole itself becomes the attractor or neither of these things (which would mean either a waste of half a year's work or something totally cool and new).

I'll let you know next week hopefully and also provide you will the full bifurcation diagram.