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A suspension flow with a Plykin attractor
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Ru, LinLing (2013) A suspension flow with a Plykin attractor. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2709486~S1
Abstract
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.
Item Type: | Thesis (PhD) |
---|---|
Subjects: | Q Science > QA Mathematics |
Library of Congress Subject Headings (LCSH): | Attractors (Mathematics), Vector fields |
Official Date: | June 2013 |
Institution: | University of Warwick |
Theses Department: | Mathematics Institute |
Thesis Type: | PhD |
Publication Status: | Unpublished |
Supervisor(s)/Advisor: | MacKay, R. S. (Robert Sinclair) |
Sponsors: | Warwick Postgraduate Research Scholarship |
Extent: | ix, 93 leaves. |
Language: | eng |
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