Weierstrass integrability of differential equations

2009/09/01 by Jaume Giné, Giné, Jaume, Maite Grau +1
Mathematics · #34C05 #34C23 #37G15 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:34C05 #msc:34C23 #msc:37G15

paper · pdf · doi:10.48550/arxiv.0909.0113

6 pages, no figures

arxiv created 2009/09/01 · arxiv updated 2009/12/01

Abstract

The integrability problem consists in finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterization of systems which admit an elementary or Liouvillian first integral. We define \it Weierstrass integrability and we determine which Weierstrass integrable systems are Liouvillian integrable. Inside this new class of integrable systems there are non--Liouvillian integrable systems.

Related

• Liouvillian integrability of polynomial differential systems
• Linearizable ordinary differential equations
• Reduction of Elementary Integrability of Polynomial Vector Fields
• Integrability and solvability of polynomial Liénard differential systems
• A new family of integrable differential systems in arbitrary dimension