On algebraic relations between solutions of a generic Painlevé equation

DOI10.1515/crelle-2014-0082zbMath1385.34068arXiv1112.2916OpenAlexW3104609443MaRDI QIDQ524582

Joel Nagloo, Anand Pillay

Publication date: 3 May 2017

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.2916

zbMATH Keywords

algebraically dependent over \(\mathbb{C}(t)\)

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

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Autonomous first order differential equations ⋮ On transformations in the Painlevé family ⋮ Some functional transcendence results around the Schwarzian differential equation ⋮ Generic differential equations are strongly minimal ⋮ Algebraic independence of generic Painlevé transcendents: PIII and PVI ⋮ Internality of logarithmic-differential pullbacks ⋮ Ax-Lindemann-Weierstrass with derivatives and the genus 0 Fuchsian groups ⋮ Geometric triviality of the strongly minimal second Painlevé equations ⋮ Ax-Schanuel and strong minimality for the \(j\)-function ⋮ TURING DEGREE SPECTRA OF DIFFERENTIALLY CLOSED FIELDS ⋮ Rational factors, invariant foliations and algebraic disintegration of compact mixing Anosov flows of dimension \(3\) ⋮ Variations for some Painlevé equations ⋮ Painlevé equation PII and strongly normal extensions ⋮ Effective definability of Kolchin polynomials ⋮ Corps différentiels et flots géodésiques I : Orthogonalité aux constantes pour les équations différentielles autonomes ⋮ Generic planar algebraic vector fields are strongly minimal and disintegrated ⋮ When any three solutions are independent ⋮ Finiteness theorems on hypersurfaces in partial differential-algebraic geometry

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