University of Illinois Urbana-Champaign

The order of growth of the fourth painleve transcendents

Sriponpaew, Boonyong

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Sriponpaew_Boonyong.pdf

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https://hdl.handle.net/2142/30907

Description

Title
The order of growth of the fourth painleve transcendents
Author(s)
Sriponpaew, Boonyong
Issue Date
2012-05-22T00:14:28Z
Director of Research (if dissertation) or Advisor (if thesis)
Hinkkanen, Aimo
Committee Member(s)
  • Hinkkanen, Aimo
  • Loeb, Peter
  • Nikolaev, Igor
  • Miles, Joseph B.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2012-05-22T00:14:28Z
Keyword(s)
  • fourth Painlevé equation
  • order of growth
Abstract
Let w be a transcendental solution of the fourth Painlevé equation w00 = (w0)2 2w + 3 2 w3 + 4zw2 + 2(z2 􀀀 )w + w : It has a rst integral w02 = w4 + 4zw3 + 4(z2 􀀀 )w2 􀀀 2 􀀀 4wU; where the auxilliary function U satis es U0 = w2 + 2zw: We will consider three speci c cases of limit behaviors of the auxiliary function U outside certain exceptional sets. In each case, we conclude that w is either of order (w) = 2 or of order (w) = 4: ii
Graduation Semester
2012-05
Permalink
http://hdl.handle.net/2142/30907
Copyright and License Information
Copyright 2012 Boonyong Sriponpaew

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