arXiv subjects

S. Walcher

Publications and source records attributed to S. Walcher.

4 recordsLinked to original sources

arXiv2014

Side conditions for ordinary differential equations

We specialize Olver's and Rosenau's side condition heuristics for the determination of particular invariant sets of ordinary differential equations. It turns out that side conditions of so-called LaSalle type are of special interest. Moreover we put side condition properties of symmetric and partially symmetric equations in a wider context. In the final section we present an application to parameter-dependent systems, in particular to quasi-steady state for chemical reactions.

math.DS↗

arXiv2013

Convergence of normal form transformations: The role of symmetries

We discuss the convergence problem for coordinate transformations which take a given vector field into Poincaré-Dulac normal form. We show that the presence of linear or nonlinear Lie point symmetries can guaranteee convergence of these normalizing transformations, in a number of scenarios. As an application, we consider a class of bifurcation problems.

math-ph↗

arXiv2005

Dimension increase and splitting for Poincare'-Dulac normal forms

Integration of nonlinear dynamical systems is usually seen as associated to a symmetry reduction, e.g. via momentum map. In Lax integrable systems, as pointed out by Kazhdan, Kostant and Sternberg in discussing the Calogero system, one proceeds in the opposite way, enlarging the nonlinear system to a system of greater dimension. We discuss how this approach is also fruitful in studying non integrable systems, focusing on systems in normal form.

math-ph↗

arXiv2001

Linear Lie algebras with finite dimensional centralizers

We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario some applications to normal forms and to certain equations with fundamental solutions are presented.

math-ph↗