The order of growth of the fourth painleve transcendents

Sriponpaew, Boonyong

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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

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

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

Copyright and License Information

Copyright 2012 Boonyong Sriponpaew

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