Indiana University-Purdue University Indianapolis (IUPUI) / 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.
| Identifer | oai:union.ndltd.org:IUPUI/oai:scholarworks.iupui.edu:1805/19905 |
| Date | 08 1900 |
| Creators | Prokhorov, Andrei |
| Contributors | Its, Alexander, Bleher, Pavel, Eremenko, Alexandre, Tarasov, Vitaly |
| Source Sets | Indiana University-Purdue University Indianapolis |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Rights | Attribution 3.0 United States, http://creativecommons.org/licenses/by/3.0/us/ |
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