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Title: A suspension flow with a Plykin attractor
Author: Ru, LinLing
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2013
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In this thesis we construct a vector field ~s* on ^CxS1 with a period-one and a period-three repelling orbit. This vector field is real analytic everywhere except on these two special orbits. We will show that on the vector field ~s* there exists a region of uniform hyperbolicity and neighbourhoods of repulsion near the two special orbits, and we have a conjecture that we can enlarge the region of uniform hyperbolicity and the neighbourhoods of repulsion so that they cover the whole space ^C x S1. We prove that if the conjecture is true then there exists a suspended Plykin attractor for the vector field ~s*. We briefly outline the contents of this thesis. The first chapter reviews the basic concepts and tools for the constructions and proofs in the later chapters. The second chapter introduces the original Plykin attractor and a modern construction of the Plykin attractor on a plane in discrete time. In the third chapter we give a construction of the Plykin attractor in continuous time, the vector field ~s* on ^CxS1. The fourth chapter discusses and provides the proofs of some properties of ~s*. The last chapter gives a summary of the construction and contains some discussions on how to make the vector field real analytic on the whole of ^C x S1.
Supervisor: Not available Sponsor: Warwick Postgraduate Research Scholarship
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics