Double covering of the Painlev\'e I equation and its singular analysis
Abstract
In this note, we will do analysis of accessible singular points for a polynomial Hamiltonian system obtained by taking a double covering of the Painlev\'e I equation. We will show that this system passes the Painlev\'e α-test for all accessible singular points Pi \ (i=1,2,3). We note its holomorphy condition of the first Painlev\'e system.
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