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Mathematics > Classical Analysis and ODEs

arXiv:2201.03838 (math)
[Submitted on 11 Jan 2022]

Title:On the equations of Poizat and Liénard

Authors:James Freitag, Rémi Jaoui, David Marker, Joel Nagloo
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Abstract:We study the structure of the solution sets in universal differential fields of certain differential equations of order two, the Poizat equations, which are particular cases of Liénard equations. We give a necessary and sufficient condition for strong minimality for equations in this class and a complete classification of the algebraic relations for solutions of strongly minimal Poizat equations. We also give an analysis of the non strongly minimal cases as well as applications concerning the Liouvillian and Pfaffian solutions of some Liénard equations.
Comments: 49 pages
Subjects: Classical Analysis and ODEs (math.CA); Algebraic Geometry (math.AG); Logic (math.LO)
MSC classes: 34M15, 12H05, 03C60
Cite as: arXiv:2201.03838 [math.CA]
  (or arXiv:2201.03838v1 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.2201.03838

Submission history

From: Remi Jaoui [view email]
[v1] Tue, 11 Jan 2022 08:44:22 UTC (47 KB)
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