Papers by Sebastian Walcher
Wechselwirkung von Populationen in einem begrenzten Lebensraum : Modellierung, Simulation und mathematische Analyse im Unterricht
Mathematics in school and readiness for university
Orbital symmetries of first order ODEs
On Sums of Vector Fields
Results in Mathematics, 1997
ABSTRACT
On monocomposition algebras
Proceedings of the American Mathematical Society, 1995
On algebras of rank three
Http Dx Doi Org 10 1080 00927879908826635, Jun 27, 2007
Error Estimatesfor Linear Compartmental Systems
SIAM Journal on Matrix Analysis and Applications, 2002
ABSTRACT
Motion in a Symmetric Potential on the Hyperbolic Plane
Canadian Journal of Mathematics, 2013
A deformation of the standard prolongation operation, defined on sets of vector fields in involut... more A deformation of the standard prolongation operation, defined on sets of vector fields in involution rather than on single ones, was recently introduced and christened "\sigma-prolongation"; correspondingly one has "\sigma-symmetries" of differential equations. These can be used to reduce the equations under study, but the general reduction procedure under \sigma-symmetries fails for equations of order one. In this note we discuss how \sigma-symmetries can be used to reduce dynamical systems, i.e. sets of first order ODEs in the form dx^a/dt = f^a (x).
We consider a deformation of the prolongation operation, defined on sets of vector fields and inv... more We consider a deformation of the prolongation operation, defined on sets of vector fields and involving a mutual interaction in the definition of prolonged ones. This maintains the "invariants by differentiation" property, and can hence be used to reduce ODEs satisfying suitable invariance conditions in a fully algorithmic way, similarly to what happens for standard prolongations and symmetries.
Journal of Lie Theory, Oct 11, 2012
We review the notion of reducibility and we introduce and discuss the notion of orbital reducibil... more We review the notion of reducibility and we introduce and discuss the notion of orbital reducibility for autonomous ordinary differential equations of first order. The relation between (orbital) reducibility and (orbital) symmetry is investigated and employed to construct (orbitally) reducible systems. By standard identifications, the notions extend to non-autonomous ODEs of first and higher order. Moreover we thus obtain a generalization of the lambda symmetries of Muriel and Romero. Several examples are given.
On differential equations in normal form
A generalization of ?-symmetry reduction for systems of ODEs: s-symmetries
J Phys a Math Theor, 2012
A radical for arbitrary algebras
Commun Algebra, 1995
ABSTRACT
A characterization of regular jordan pairs and its application to riccati differential equations
Commun Algebra, 1986
On the Poincare Problem
J Differential Equations, 2000
On a class of inversions
Http Dx Doi Org 10 1080 00927879208824469, Jun 27, 2007
�ber polynomiale, insbesondere Riccatische, Differentialgleichungen mit Fundamentall�sungen
Math Ann, 1986
Local Darboux first integrals of analytic differential systems
Bulletin Des Sciences Mathematiques, 2014
ABSTRACT
This is a collection of results on the use of innitesimal orbital symmetries of rst-order ordinar... more This is a collection of results on the use of innitesimal orbital symmetries of rst-order ordinary dieren tial equations. Some of these results are classical, dating back to Lie and Bianchi, and some new results are added.
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Papers by Sebastian Walcher