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Morales-Ramis Theorems via Malgrange pseudogroup

Guy Casale (2009)

Annales de l’institut Fourier

In this article we give an obstruction to integrability by quadratures of an ordinary differential equation on the differential Galois group of variational equations of any order along a particular solution. In Hamiltonian situation the condition on the Galois group gives Morales-Ramis-Simó theorem. The main tools used are Malgrange pseudogroup of a vector field and Artin approximation theorem.

Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion

Tetsuya Ishiwata (2015)

Mathematica Bohemica

We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never...

Nonuniqueness results for ordinary differential equations

Josef Kalas (1998)

Czechoslovak Mathematical Journal

In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of Chr. Nowak, of Samimi’s nonuniqueness theorem and of Stettner’s nonuniqueness criterion.

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