Analytic study of Painleve equations and a nelated clans of equation

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1. We found a class of nonlinear ordinary differential equations containing the first Painleve equation such that each equation admits the quasi-Painleve property, and discussed the global multi-valuedness of their solutions. We also found a similar clean of equations containing the second Painleve equation.2. For solutions of the fifth Painleve equation, we examined value distribution in a sectonial domain. Under a certain condition, we proved the equi-distribution of values.3. For a degenerate Garnier system corresponding to the first Painleve equation, we obtain an asymptotic solution around a singular locus.4. We examined algebraic independence and algebraic relations for reciprocal rums of Fibonacci numbers. We also discussed their relation to zeta values.