Connection Problem for Painlevé Tau Functions

We derive the differential identities for isomonodromic tau functions, describing their monodromy dependence. For Painlev´e equations we obtain them from the relation of tau function to classical action which is a consequence of quasihomogeneity of corresponding Hamiltonians. We use these identities to solve the connection problem for generic solution of Painlev´e-III(D8) equation, and homogeneous Painlev´e-II equation. We formulate conjectures on Hamiltonian and symplectic structure of general isomonodromic deformations we obtained during our studies and check them for Painlev´e equations.

Author dc:creator

• Prokhorov, Andrei

Advisor dc:contributor.advisor

• Its, Alexander

• isomonodromic tau function
• connection problem
• Hamiltonian systems
• classical action
• Riemann-Hilbert correspondence
• isomonodromic deformations
• quasihomogeneous functions
• Painlevé equations

Statement dc:rights

• Attribution 3.0 United States

Licence dc:rights.uri

• http://creativecommons.org/licenses/by/3.0/us/

Language dc:language.iso

en_US

DOI

10.7912/rygf-2h27

Identifier URI

http://dx.doi.org/10.7912/rygf-2h27
http://dx.doi.org/10.7912/C2/2405

OAI identifier oai:identifier

oai:scholarworks.indianapolis.iu.edu:1805/19905