COURSES
The subject of this project is the proof of the C1 Stability Conjecture as given by Ricardo Mañe, first published in 1988. Although Mañe’s proof established it as a theorem its statement became famous under the name of C1 Stability Conjecture, hence I kept the term conjecture rather than theorem.
CONFERENCES
Chapter two starts with a general presentation of the concept of structural stability and an overview of the formal mathematical language developed to describe it. I introduce the C1 Stability Conjecture and its important role in unifying many results that attempted to describe and classify dynamical systems.
WORKSHOPS
The proof of the C1 Stability Conjecture is an elaborate and complex construction based on six main theorems and four supporting lemmas. The objective of my work was first to collect and familiarise myself with all the key concepts and ingredients necessary for understanding the proof. Mañe’s proof uses results developed by other famous mathematicians who made sustained efforts towards solving it.
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Chapter three contains outline of the proof where I present for each theorem and lemma, the scope and the rationale behind introducing those particular results. It also identifies the steps of the proof and how the requirement of the proof is being reduced from one statement to another. I have also enclosed a flowchart of the proof, which contains minimum details to help the reader follow the argument but not so much as to detract from understanding the overall strategy.
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