publication . Article . 2001

The discrete Painlevé I equations: transcendental integrability and asymptotic solutions

M Bernardo; T T Truong; G Rollet;
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  • Published: 13 Aug 2001 Journal: Journal of Physics A: Mathematical and General, volume 34, pages 3,215-3,252 (issn: 0305-4470, eissn: 1361-6447, Copyright policy)
  • Publisher: IOP Publishing
Abstract
According to the scheme of equation (2.14) the iteration of Φ yields only a minimal factorization. In fact, one should have: where P is a polynomial. Hence equation (2.15) should be replaced by an inequality  . Thus the estimation derived from the generating function g is an upper bound for the algebraic entropy, which should be zero for m = 1 since a parametrization of the transformation is given. These observations are also valid for the equations (3.16) and (4.14).
Subjects
free text keywords: Mathematical Physics, General Physics and Astronomy, Statistical and Nonlinear Physics, Generating function, Factorization, Polynomial, Transcendental number, Parametrization, Algebraic number, Mathematical analysis, Upper and lower bounds, Mathematics
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