Year: 2014
Type: article
Abstract: In the present paper, we prove that if y ′′ = f ( y , y ′ , t , α , β , … ) ${y^{\prime\prime}\hskip-0.569055pt=\hskip-0.569055ptf(y,y^{\prime},t,\alpha,% \beta,\ldots)}$ is a “generic” Painlevé equation (that is, an equation in one of the families P I ${P_{\rm I}}$ – P VI ${P_{\rm VI}}$ but with the relevant complex parameters α , β , … ${\alpha,\beta,\ldots}$ algebraically independent), and if y 1 , … , y n ${y_{1},\ldots,y_{n}}$ are solutions such that y 1 , y 1 ′ , y 2 , y 2 ′ , … , y n , y n ′ $y_{1},y_{1}^{\prime},y_{2},y_{2}^{\prime},\ldots,y_{n},y_{n}^{\prime}$ are algebraically dependent over ℂ ( t ) ${{\mathbb{C}}(t)}$ , then already for some 1 ≤ i < j ≤ n ${1\leq i , y i , y i ′ , y j , y j ′ ${y_{i},y_{i}^{\prime},y_{j},y_{j}^{\prime}}$</
Authors: Joel Nagloo, Anand Pillay
Institutions: University of Leeds, University of Notre Dame
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G5940767488
OpenAlex ID: W2035959274