The order of growth of the fourth painleve transcendents

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

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Sriponpaew, Boonyong

Contributors dc:contributor

• Hinkkanen, Aimo
• Loeb, Peter
• Nikolaev, Igor
• Miles, Joseph B.

• order of growth
• fourth Painlevé equation

Statement dc:rights

• Copyright 2012 Boonyong Sriponpaew

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/30907